Mathematics Branches, Topics, and Sub-Topics

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28Bxx Set functions and measures with values in abstract spaces

This subtopic studies set functions and measures with values in abstract spaces, extending measure-theoretic ideas beyond real-valued settings.

Specific topics

28B05 Vector-valued set functions, measures and integrals

Overview

28B05 studies vector-valued set functions, measures and integrals in set functions and measures with values in abstract spaces. It studies measures and set functions taking values in vector spaces or other abstract targets rather than the real line.

Related Wikipedia Page

Set Functions And Measures With Values In Abstract Spaces (Wikipedia)

Useful Links

Key Ideas

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

Typical Uses

Used in vector-measure theory, Banach-space methods, and abstract integration.

Applications

  • Vector measures
  • Abstract integration
  • Banach-space applications

References

Recommended Textbooks

28B10 Group- or semigroup-valued set functions and measures

Overview

28B10 studies group- or semigroup-valued set functions and measures in set functions and measures with values in abstract spaces. It studies measures and set functions taking values in vector spaces or other abstract targets rather than the real line.

Related Wikipedia Page

Set Functions And Measures With Values In Abstract Spaces (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for group- or semigroup-valued set functions and measures
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in vector-measure theory, Banach-space methods, and abstract integration.

Applications

  • Vector measures
  • Abstract integration
  • Banach-space applications

References

Recommended Textbooks

28B15 Set functions and measures with values in ordered spaces

Overview

28B15 studies set functions and measures with values in ordered spaces in set functions and measures with values in abstract spaces. It studies measures and set functions taking values in vector spaces or other abstract targets rather than the real line.

Related Wikipedia Page

Set Functions And Measures With Values In Abstract Spaces (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for set functions and measures with values in ordered 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 vector-measure theory, Banach-space methods, and abstract integration.

Applications

  • Vector measures
  • Abstract integration
  • Banach-space applications

References

Recommended Textbooks

28B20 Set-valued set functions and measures; integration of set-valued functions

Overview

28B20 studies set-valued set functions and measures; integration of set-valued functions in set functions and measures with values in abstract spaces. It studies measures and set functions taking values in vector spaces or other abstract targets rather than the real line.

Related Wikipedia Page

Set Functions And Measures With Values In Abstract Spaces (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for set-valued set functions and measures; integration of set-valued functions
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in vector-measure theory, Banach-space methods, and abstract integration.

Applications

  • Vector measures
  • Abstract integration
  • Banach-space applications

References

Recommended Textbooks