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4 - Abstract Measures

from PART I - Measure And Integration

Published online by Cambridge University Press:  06 January 2022

Martin Buntinas
Martin Buntinas
Affiliation:
Loyola University, Chicago
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Summary

This chapter extends Lebesgue measure to Abstract Measure Spaces. Example such as Lebesgue-Stieltjes Measures, Probability Measures, and Signed Measures are considered. The Radon–Nikodym Theorem on Absolute Continuity is proven. The Radon–Nikodym derivative is defined and its Chain Rule is proven.

Keywords

Abstract Measure SpaceLebesgue–Stieltjes MeasureProbability MeasureSigned MeasureAbsolute ContinuityRadon–Nikodym
Type
Chapter
Information
Classical and Discrete Functional Analysis with Measure Theory , pp. 136 - 166
Publisher: Cambridge University Press
Print publication year: 2022

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  • Abstract Measures
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.007
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  • Abstract Measures
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.007
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Abstract Measures
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.007
Available formats
×