28Axx Classical measure theory
This subtopic studies classical measure theory, focusing on measurable sets, measures, integration, and foundational results such as convergence theorems.
Specific topics
28A05 Classes of sets (Borel fields, etc.), measurable sets
Overview
28A05 studies classes of sets (borel fields, etc.), measurable sets in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for classes of sets (borel fields, etc.), measurable sets
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A10 Real- or complex-valued set functions
Overview
28A10 studies real- or complex-valued set functions in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for real- or complex-valued set functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A12 Contents, measures, outer measures, capacities
Overview
28A12 studies contents, measures, outer measures, capacities in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for contents, measures, outer measures, capacities
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A15 Abstract differentiation theory, differentiation of set functions
Overview
28A15 studies abstract differentiation theory, differentiation of set functions in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for abstract differentiation theory, differentiation of set functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A20 Measurable and nonmeasurable functions, sequences of measurable functions
Overview
28A20 studies measurable and nonmeasurable functions, sequences of measurable functions in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for measurable and nonmeasurable functions, sequences of measurable functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A25 Integration theory
Overview
28A25 studies integration theory in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integration theory
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A33 Spaces of measures, convergence of measures
Overview
28A33 studies spaces of measures, convergence of measures in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for spaces of measures, convergence of measures
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A35 Measures and integrals in product spaces
Overview
28A35 studies measures and integrals in product spaces in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for measures and integrals in product spaces
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A50 Integration and disintegration of measures
Overview
28A50 studies integration and disintegration of measures in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integration and disintegration of measures
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A51 Lifting theory
Overview
28A51 studies lifting theory in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for lifting theory
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A60 Measures on Boolean rings, measure algebras
Overview
28A60 studies measures on boolean rings, measure algebras in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for measures on boolean rings, measure algebras
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A75 Length, area, volume, other geometric measure theory
Overview
28A75 studies length, area, volume, other geometric measure theory in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for length, area, volume, other geometric measure theory
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A78 Hausdorff and packing measures
Overview
28A78 studies hausdorff and packing measures in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for hausdorff and packing measures
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks
28A80 Fractals
Overview
28A80 studies fractals in classical measure theory. It studies sigma-algebras, measures, integration, and convergence theorems in the classical Lebesgue framework.
Related Wikipedia Page
Classical Measure Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for fractals
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to build integration theory and probabilistic foundations in analysis.
Applications
- Lebesgue integration
- Probability foundations
- Limit and convergence theorems
References
Recommended Textbooks