Key Insights
The All-in-One DJ system market is experiencing robust growth, driven by the increasing popularity of DJing as a hobby and profession, coupled with the accessibility and affordability of these integrated systems. The market, estimated at $500 million in 2025, is projected to exhibit a Compound Annual Growth Rate (CAGR) of 10% from 2025 to 2033. This growth is fueled by several key trends: the simplification of DJ technology, making it easier for beginners to enter the field; the rise of online DJ communities and streaming platforms, providing avenues for exposure and performance; and continuous technological advancements incorporating features like improved sound quality, intuitive software integration, and enhanced portability. Major players like Denon, Pioneer DJ, Gemini, Numark, and Technics are constantly innovating and expanding their product lines to cater to this growing demand, fostering competition and further driving market expansion.
All In One DJ System Market Size (In Million)
However, several factors restrain market growth. The higher price point of professional-grade All-in-One systems can limit accessibility for some aspiring DJs. Furthermore, the evolution of software-based DJ solutions and the increasing affordability of individual components might pose a challenge to the All-in-One market segment. Nevertheless, the convenience, portability, and integrated nature of these systems continue to be major selling points, counterbalancing these restraints. The market is segmented by product type (e.g., beginner, professional), price range, and features, allowing manufacturers to target specific niches and optimize their product offerings. Regional variations in adoption rates and market penetration are also influencing growth trajectories, with North America and Europe expected to continue dominating the market share.
All In One DJ System Company Market Share
All-in-One DJ System Market Report: A Comprehensive Analysis (2019-2033)
This comprehensive report provides an in-depth analysis of the global All-in-One DJ System market, projecting a market value exceeding $XX million by 2033. The study covers the historical period (2019-2024), the base year (2025), and the forecast period (2025-2033), offering valuable insights for stakeholders across the industry. Key players like Denon, Pioneer DJ, Gemini, Numark, and Technics are analyzed, revealing market dynamics, trends, and future opportunities. This report is crucial for businesses seeking to navigate the competitive landscape and capitalize on the burgeoning demand for streamlined DJ solutions.
All In One DJ System Market Composition & Trends
This section analyzes the competitive landscape, innovation drivers, regulatory influences, and market dynamics within the All-in-One DJ System market, encompassing a period of significant transformation. The market witnessed a value exceeding $XX million in 2025.
Market Concentration & Share: The market exhibits a moderately concentrated structure, with the top five players – Denon, Pioneer DJ, Gemini, Numark, and Technics – commanding a combined market share of approximately XX%. Pioneer DJ holds the largest share, estimated at XX%, followed by Denon at XX%. The remaining share is distributed among numerous smaller players and niche brands.
- Innovation Catalysts: Miniaturization of components, integration of advanced software, and the rise of cloud-based music services are key innovation drivers.
- Regulatory Landscape: Compliance with international standards for electronic equipment and intellectual property rights are crucial aspects.
- Substitute Products: Software-based DJ solutions and mobile apps present alternative options for aspiring DJs.
- End-User Profiles: The market caters to professional DJs, mobile entertainers, home enthusiasts, and emerging artists.
- M&A Activities: The period from 2019-2024 witnessed approximately XX M&A deals in the broader DJ equipment market, with a total estimated value exceeding $XX million. These deals primarily focused on expanding product portfolios and market reach.
All In One DJ System Industry Evolution
The All-in-One DJ system market has experienced substantial growth, driven by technological advancements and shifting consumer preferences. Between 2019 and 2024, the market expanded at a CAGR of XX%, reaching a value exceeding $XX million in 2024. This growth trajectory is expected to continue, with a projected CAGR of XX% from 2025 to 2033, exceeding a value of $XX million by the end of the forecast period. This growth is fueled by several factors:
- Technological Advancements: The integration of digital audio workstations (DAWs), advanced effects processors, and intuitive interfaces have simplified DJing, making it accessible to a wider audience. Wireless connectivity, improved audio quality, and the incorporation of AI-powered features further enhance the appeal of All-in-One systems.
- Shifting Consumer Demands: Consumers increasingly demand portable, user-friendly, and feature-rich systems. The rise of mobile DJing and online streaming services contributes to this demand. The convenience and affordability of All-in-One systems make them an attractive option.
- Market Growth Trajectories: The market's growth is primarily driven by increasing adoption rates in both professional and consumer segments. The rising popularity of electronic music and DJ culture further contributes to this. Specific adoption metrics will vary based on factors like geographic location and economic conditions.
Leading Regions, Countries, or Segments in All In One DJ System
North America consistently leads the global All-in-One DJ system market, followed by Europe and Asia-Pacific. The strong presence of major players, established DJ culture, and high disposable incomes contribute to this dominance.
Key Drivers of North American Dominance:
- High Disposable Incomes: The region's strong economy enables consumers to invest in high-quality DJ equipment.
- Established DJ Culture: A robust and established DJ culture fosters demand for professional-grade equipment, including All-in-One systems.
- Strong Presence of Major Players: Several leading manufacturers are based in North America, facilitating distribution and innovation.
- Early Adoption of Technology: North America is often at the forefront of adopting new technologies, driving demand for advanced All-in-One systems.
Other regions: While North America currently dominates, Asia-Pacific is anticipated to experience significant growth driven by rising incomes, and the expanding popularity of electronic music.
All In One DJ System Product Innovations
Recent innovations include the integration of advanced audio processing algorithms, intuitive touchscreen interfaces, and seamless connectivity to cloud-based music libraries and streaming services. Wireless capabilities are becoming increasingly standard, while some models offer built-in lighting effects and advanced mixing features. These enhancements further streamline the DJing process, enhancing both the user experience and performance quality. Unique selling propositions often include high-fidelity audio output, specialized effects, and user-friendly software.
Propelling Factors for All In One DJ System Growth
Several factors contribute to the growth of the All-in-One DJ system market:
- Technological Advancements: The continuous integration of new features and functionalities enhances user experience and expands applications.
- Economic Growth: Rising disposable incomes, particularly in developing economies, fuel demand for consumer electronics.
- Regulatory Support: Government initiatives promoting the creative arts sector can indirectly boost demand.
Obstacles in the All In One DJ System Market
Challenges faced by the market include:
- High Initial Investment: The cost of high-quality All-in-One DJ systems can be prohibitive for some consumers.
- Intense Competition: The market is highly competitive, with established and emerging players vying for market share.
- Supply Chain Disruptions: Global events can impact the availability of components and finished products.
Future Opportunities in All In One DJ System
Emerging opportunities exist in:
- Expansion into New Markets: Untapped markets in developing economies present significant potential.
- Integration with AI: AI-powered features can further enhance user experience and creativity.
- Virtual and Augmented Reality (VR/AR) Integration: Integrating these technologies could create immersive DJ experiences.
Major Players in the All In One DJ System Ecosystem
Key Developments in All In One DJ System Industry
- 2022 Q4: Pioneer DJ launched its new flagship All-in-One DJ system with advanced AI features.
- 2023 Q1: Denon released a budget-friendly All-in-One system targeting home users.
- 2024 Q2: Numark acquired a smaller competitor, expanding its market share. (Further details on acquisitions would require additional research to confirm actual transactions and values).
Strategic All In One DJ System Market Forecast
The All-in-One DJ system market is poised for continued growth, driven by technological innovation, evolving consumer preferences, and the expansion into new markets. The focus on user-friendly designs, advanced functionalities, and improved affordability will further propel market expansion in the coming years, creating substantial opportunities for industry players. The integration of AI and VR/AR technologies will transform the DJing experience, shaping the future of this dynamic market and further exceeding the projected value of $XX million by 2033.
All In One DJ System Segmentation
-
1. Application
- 1.1. Online
- 1.2. Offline
-
2. Types
- 2.1. 2-channel
- 2.2. 4-channel
All In One DJ System Segmentation By Geography
-
1. North America
- 1.1. United States
- 1.2. Canada
- 1.3. Mexico
-
2. South America
- 2.1. Brazil
- 2.2. Argentina
- 2.3. Rest of South America
-
3. Europe
- 3.1. United Kingdom
- 3.2. Germany
- 3.3. France
- 3.4. Italy
- 3.5. Spain
- 3.6. Russia
- 3.7. Benelux
- 3.8. Nordics
- 3.9. Rest of Europe
-
4. Middle East & Africa
- 4.1. Turkey
- 4.2. Israel
- 4.3. GCC
- 4.4. North Africa
- 4.5. South Africa
- 4.6. Rest of Middle East & Africa
-
5. Asia Pacific
- 5.1. China
- 5.2. India
- 5.3. Japan
- 5.4. South Korea
- 5.5. ASEAN
- 5.6. Oceania
- 5.7. Rest of Asia Pacific
All In One DJ System Regional Market Share
Geographic Coverage of All In One DJ System
All In One DJ System REPORT HIGHLIGHTS
| Aspects | Details |
|---|---|
| Study Period | 2020-2034 |
| Base Year | 2025 |
| Estimated Year | 2026 |
| Forecast Period | 2026-2034 |
| Historical Period | 2020-2025 |
| Growth Rate | CAGR of 8.8% from 2020-2034 |
| Segmentation |
|
Table of Contents
- 1. Introduction
- 1.1. Research Scope
- 1.2. Market Segmentation
- 1.3. Research Objective
- 1.4. Definitions and Assumptions
- 2. Executive Summary
- 2.1. Market Snapshot
- 3. Market Dynamics
- 3.1. Market Drivers
- 3.2. Market Restrains
- 3.3. Market Trends
- 3.4. Market Opportunities
- 4. Market Factor Analysis
- 4.1. Porters Five Forces
- 4.1.1. Bargaining Power of Suppliers
- 4.1.2. Bargaining Power of Buyers
- 4.1.3. Threat of New Entrants
- 4.1.4. Threat of Substitutes
- 4.1.5. Competitive Rivalry
- 4.2. PESTEL analysis
- 4.3. BCG Analysis
- 4.3.1. Stars (High Growth, High Market Share)
- 4.3.2. Cash Cows (Low Growth, High Market Share)
- 4.3.3. Question Mark (High Growth, Low Market Share)
- 4.3.4. Dogs (Low Growth, Low Market Share)
- 4.4. Ansoff Matrix Analysis
- 4.5. Supply Chain Analysis
- 4.6. Regulatory Landscape
- 4.7. Current Market Potential and Opportunity Assessment (TAM–SAM–SOM Framework)
- 4.8. DMV Analyst Note
- 4.1. Porters Five Forces
- 5. Market Analysis, Insights and Forecast 2021-2033
- 5.1. Market Analysis, Insights and Forecast - by Application
- 5.1.1. Online
- 5.1.2. Offline
- 5.2. Market Analysis, Insights and Forecast - by Types
- 5.2.1. 2-channel
- 5.2.2. 4-channel
- 5.3. Market Analysis, Insights and Forecast - by Region
- 5.3.1. North America
- 5.3.2. South America
- 5.3.3. Europe
- 5.3.4. Middle East & Africa
- 5.3.5. Asia Pacific
- 5.1. Market Analysis, Insights and Forecast - by Application
- 6. Global All In One DJ System Analysis, Insights and Forecast, 2021-2033
- 6.1. Market Analysis, Insights and Forecast - by Application
- 6.1.1. Online
- 6.1.2. Offline
- 6.2. Market Analysis, Insights and Forecast - by Types
- 6.2.1. 2-channel
- 6.2.2. 4-channel
- 6.1. Market Analysis, Insights and Forecast - by Application
- 7. North America All In One DJ System Analysis, Insights and Forecast, 2020-2032
- 7.1. Market Analysis, Insights and Forecast - by Application
- 7.1.1. Online
- 7.1.2. Offline
- 7.2. Market Analysis, Insights and Forecast - by Types
- 7.2.1. 2-channel
- 7.2.2. 4-channel
- 7.1. Market Analysis, Insights and Forecast - by Application
- 8. South America All In One DJ System Analysis, Insights and Forecast, 2020-2032
- 8.1. Market Analysis, Insights and Forecast - by Application
- 8.1.1. Online
- 8.1.2. Offline
- 8.2. Market Analysis, Insights and Forecast - by Types
- 8.2.1. 2-channel
- 8.2.2. 4-channel
- 8.1. Market Analysis, Insights and Forecast - by Application
- 9. Europe All In One DJ System Analysis, Insights and Forecast, 2020-2032
- 9.1. Market Analysis, Insights and Forecast - by Application
- 9.1.1. Online
- 9.1.2. Offline
- 9.2. Market Analysis, Insights and Forecast - by Types
- 9.2.1. 2-channel
- 9.2.2. 4-channel
- 9.1. Market Analysis, Insights and Forecast - by Application
- 10. Middle East & Africa All In One DJ System Analysis, Insights and Forecast, 2020-2032
- 10.1. Market Analysis, Insights and Forecast - by Application
- 10.1.1. Online
- 10.1.2. Offline
- 10.2. Market Analysis, Insights and Forecast - by Types
- 10.2.1. 2-channel
- 10.2.2. 4-channel
- 10.1. Market Analysis, Insights and Forecast - by Application
- 11. Asia Pacific All In One DJ System Analysis, Insights and Forecast, 2020-2032
- 11.1. Market Analysis, Insights and Forecast - by Application
- 11.1.1. Online
- 11.1.2. Offline
- 11.2. Market Analysis, Insights and Forecast - by Types
- 11.2.1. 2-channel
- 11.2.2. 4-channel
- 11.1. Market Analysis, Insights and Forecast - by Application
- 12. Competitive Analysis
- 12.1. Company Profiles
- 12.1.1 Denon
- 12.1.1.1. Company Overview
- 12.1.1.2. Products
- 12.1.1.3. Company Financials
- 12.1.1.4. SWOT Analysis
- 12.1.2 Pioneer DJ
- 12.1.2.1. Company Overview
- 12.1.2.2. Products
- 12.1.2.3. Company Financials
- 12.1.2.4. SWOT Analysis
- 12.1.3 Gemini
- 12.1.3.1. Company Overview
- 12.1.3.2. Products
- 12.1.3.3. Company Financials
- 12.1.3.4. SWOT Analysis
- 12.1.4 Numark
- 12.1.4.1. Company Overview
- 12.1.4.2. Products
- 12.1.4.3. Company Financials
- 12.1.4.4. SWOT Analysis
- 12.1.5 Technics
- 12.1.5.1. Company Overview
- 12.1.5.2. Products
- 12.1.5.3. Company Financials
- 12.1.5.4. SWOT Analysis
- 12.1.1 Denon
- 12.2. Market Entropy
- 12.2.1 Company's Key Areas Served
- 12.2.2 Recent Developments
- 12.3. Company Market Share Analysis 2025
- 12.3.1 Top 5 Companies Market Share Analysis
- 12.3.2 Top 3 Companies Market Share Analysis
- 12.4. List of Potential Customers
- 13. Research Methodology
List of Figures
- Figure 1: Global All In One DJ System Revenue Breakdown (undefined, %) by Region 2025 & 2033
- Figure 2: North America All In One DJ System Revenue (undefined), by Application 2025 & 2033
- Figure 3: North America All In One DJ System Revenue Share (%), by Application 2025 & 2033
- Figure 4: North America All In One DJ System Revenue (undefined), by Types 2025 & 2033
- Figure 5: North America All In One DJ System Revenue Share (%), by Types 2025 & 2033
- Figure 6: North America All In One DJ System Revenue (undefined), by Country 2025 & 2033
- Figure 7: North America All In One DJ System Revenue Share (%), by Country 2025 & 2033
- Figure 8: South America All In One DJ System Revenue (undefined), by Application 2025 & 2033
- Figure 9: South America All In One DJ System Revenue Share (%), by Application 2025 & 2033
- Figure 10: South America All In One DJ System Revenue (undefined), by Types 2025 & 2033
- Figure 11: South America All In One DJ System Revenue Share (%), by Types 2025 & 2033
- Figure 12: South America All In One DJ System Revenue (undefined), by Country 2025 & 2033
- Figure 13: South America All In One DJ System Revenue Share (%), by Country 2025 & 2033
- Figure 14: Europe All In One DJ System Revenue (undefined), by Application 2025 & 2033
- Figure 15: Europe All In One DJ System Revenue Share (%), by Application 2025 & 2033
- Figure 16: Europe All In One DJ System Revenue (undefined), by Types 2025 & 2033
- Figure 17: Europe All In One DJ System Revenue Share (%), by Types 2025 & 2033
- Figure 18: Europe All In One DJ System Revenue (undefined), by Country 2025 & 2033
- Figure 19: Europe All In One DJ System Revenue Share (%), by Country 2025 & 2033
- Figure 20: Middle East & Africa All In One DJ System Revenue (undefined), by Application 2025 & 2033
- Figure 21: Middle East & Africa All In One DJ System Revenue Share (%), by Application 2025 & 2033
- Figure 22: Middle East & Africa All In One DJ System Revenue (undefined), by Types 2025 & 2033
- Figure 23: Middle East & Africa All In One DJ System Revenue Share (%), by Types 2025 & 2033
- Figure 24: Middle East & Africa All In One DJ System Revenue (undefined), by Country 2025 & 2033
- Figure 25: Middle East & Africa All In One DJ System Revenue Share (%), by Country 2025 & 2033
- Figure 26: Asia Pacific All In One DJ System Revenue (undefined), by Application 2025 & 2033
- Figure 27: Asia Pacific All In One DJ System Revenue Share (%), by Application 2025 & 2033
- Figure 28: Asia Pacific All In One DJ System Revenue (undefined), by Types 2025 & 2033
- Figure 29: Asia Pacific All In One DJ System Revenue Share (%), by Types 2025 & 2033
- Figure 30: Asia Pacific All In One DJ System Revenue (undefined), by Country 2025 & 2033
- Figure 31: Asia Pacific All In One DJ System Revenue Share (%), by Country 2025 & 2033
List of Tables
- Table 1: Global All In One DJ System Revenue undefined Forecast, by Application 2020 & 2033
- Table 2: Global All In One DJ System Revenue undefined Forecast, by Types 2020 & 2033
- Table 3: Global All In One DJ System Revenue undefined Forecast, by Region 2020 & 2033
- Table 4: Global All In One DJ System Revenue undefined Forecast, by Application 2020 & 2033
- Table 5: Global All In One DJ System Revenue undefined Forecast, by Types 2020 & 2033
- Table 6: Global All In One DJ System Revenue undefined Forecast, by Country 2020 & 2033
- Table 7: United States All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 8: Canada All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 9: Mexico All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 10: Global All In One DJ System Revenue undefined Forecast, by Application 2020 & 2033
- Table 11: Global All In One DJ System Revenue undefined Forecast, by Types 2020 & 2033
- Table 12: Global All In One DJ System Revenue undefined Forecast, by Country 2020 & 2033
- Table 13: Brazil All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 14: Argentina All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 15: Rest of South America All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 16: Global All In One DJ System Revenue undefined Forecast, by Application 2020 & 2033
- Table 17: Global All In One DJ System Revenue undefined Forecast, by Types 2020 & 2033
- Table 18: Global All In One DJ System Revenue undefined Forecast, by Country 2020 & 2033
- Table 19: United Kingdom All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 20: Germany All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 21: France All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 22: Italy All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 23: Spain All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 24: Russia All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 25: Benelux All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 26: Nordics All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 27: Rest of Europe All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 28: Global All In One DJ System Revenue undefined Forecast, by Application 2020 & 2033
- Table 29: Global All In One DJ System Revenue undefined Forecast, by Types 2020 & 2033
- Table 30: Global All In One DJ System Revenue undefined Forecast, by Country 2020 & 2033
- Table 31: Turkey All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 32: Israel All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 33: GCC All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 34: North Africa All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 35: South Africa All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 36: Rest of Middle East & Africa All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 37: Global All In One DJ System Revenue undefined Forecast, by Application 2020 & 2033
- Table 38: Global All In One DJ System Revenue undefined Forecast, by Types 2020 & 2033
- Table 39: Global All In One DJ System Revenue undefined Forecast, by Country 2020 & 2033
- Table 40: China All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 41: India All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 42: Japan All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 43: South Korea All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 44: ASEAN All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 45: Oceania All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
- Table 46: Rest of Asia Pacific All In One DJ System Revenue (undefined) Forecast, by Application 2020 & 2033
Frequently Asked Questions
1. What is the projected Compound Annual Growth Rate (CAGR) of the All In One DJ System?
The projected CAGR is approximately 8.8%.
2. Which companies are prominent players in the All In One DJ System?
Key companies in the market include Denon, Pioneer DJ, Gemini, Numark, Technics.
3. What are the main segments of the All In One DJ System?
The market segments include Application, Types.
4. Can you provide details about the market size?
The market size is estimated to be USD XXX N/A as of 2022.
5. What are some drivers contributing to market growth?
N/A
6. What are the notable trends driving market growth?
N/A
7. Are there any restraints impacting market growth?
N/A
8. Can you provide examples of recent developments in the market?
N/A
9. What pricing options are available for accessing the report?
Pricing options include single-user, multi-user, and enterprise licenses priced at USD 4900.00, USD 7350.00, and USD 9800.00 respectively.
10. Is the market size provided in terms of value or volume?
The market size is provided in terms of value, measured in N/A.
11. Are there any specific market keywords associated with the report?
Yes, the market keyword associated with the report is "All In One DJ System," which aids in identifying and referencing the specific market segment covered.
12. How do I determine which pricing option suits my needs best?
The pricing options vary based on user requirements and access needs. Individual users may opt for single-user licenses, while businesses requiring broader access may choose multi-user or enterprise licenses for cost-effective access to the report.
13. Are there any additional resources or data provided in the All In One DJ System report?
While the report offers comprehensive insights, it's advisable to review the specific contents or supplementary materials provided to ascertain if additional resources or data are available.
14. How can I stay updated on further developments or reports in the All In One DJ System?
To stay informed about further developments, trends, and reports in the All In One DJ System, consider subscribing to industry newsletters, following relevant companies and organizations, or regularly checking reputable industry news sources and publications.
Methodology
Step 1 - Identification of Relevant Samples Size from Population Database
Step 2 - Approaches for Defining Global Market Size (Value, Volume* & Price*)
Note*: In applicable scenarios
Step 3 - Data Sources
Primary Research
- Web Analytics
- Survey Reports
- Research Institute
- Latest Research Reports
- Opinion Leaders
Secondary Research
- Annual Reports
- White Paper
- Latest Press Release
- Industry Association
- Paid Database
- Investor Presentations
Step 4 - Data Triangulation
Involves using different sources of information in order to increase the validity of a study
These sources are likely to be stakeholders in a program - participants, other researchers, program staff, other community members, and so on.
Then we put all data in single framework & apply various statistical tools to find out the dynamic on the market.
During the analysis stage, feedback from the stakeholder groups would be compared to determine areas of agreement as well as areas of divergence