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28Cxx Measures and integration on spaces with additional structure

This subtopic studies measures and integration on spaces with additional structure, including topological and geometric contexts.

Specific topics

28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.)

Overview

28C05 studies integration theory via linear functionals (radon measures, daniell integrals, etc.) in measures and integration on spaces with additional structure. It studies integration theory on spaces with topology, group structure, or other extra geometric data.

Related Wikipedia Page

Measures And Integration On Spaces With Additional Structure (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for integration theory via linear functionals (radon measures, daniell integrals, etc.)
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in harmonic analysis, geometric measure theory, and abstract probability.

Applications

  • Integration on topological spaces
  • Haar and invariant measures
  • Structured measure spaces

References

Recommended Textbooks

28C10 Set functions and measures on topological groups or semigroups

Overview

28C10 studies set functions and measures on topological groups or semigroups in measures and integration on spaces with additional structure. It studies integration theory on spaces with topology, group structure, or other extra geometric data.

Related Wikipedia Page

Measures And Integration On Spaces With Additional Structure (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for set functions and measures on topological groups or semigroups
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in harmonic analysis, geometric measure theory, and abstract probability.

Applications

  • Integration on topological spaces
  • Haar and invariant measures
  • Structured measure spaces

References

Recommended Textbooks

28C15 Set functions and measures on topological spaces

Overview

28C15 studies set functions and measures on topological spaces in measures and integration on spaces with additional structure. It studies integration theory on spaces with topology, group structure, or other extra geometric data.

Related Wikipedia Page

Measures And Integration On Spaces With Additional Structure (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for set functions and measures on topological spaces
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in harmonic analysis, geometric measure theory, and abstract probability.

Applications

  • Integration on topological spaces
  • Haar and invariant measures
  • Structured measure spaces

References

Recommended Textbooks

28C20 Set functions and measures and integrals in infinite-dimensional spaces

Overview

28C20 studies set functions and measures and integrals in infinite-dimensional spaces in measures and integration on spaces with additional structure. It studies integration theory on spaces with topology, group structure, or other extra geometric data.

Related Wikipedia Page

Measures And Integration On Spaces With Additional Structure (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for set functions and measures and integrals in infinite-dimensional spaces
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in harmonic analysis, geometric measure theory, and abstract probability.

Applications

  • Integration on topological spaces
  • Haar and invariant measures
  • Structured measure spaces

References

Recommended Textbooks