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2 - Lebesgue Integral

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 starts with definitions and basic properties of Measurable Functions. The Lebesgue Integral is systematically developed; first for Simple Functions, then for Nonnegative Functions, and finally for the General Case. Egorov's Theorem is proven. The important Lebesgue Limit Theorems that distinguish Lebesgue Integration from Riemann and Stieltjes Integration are discussed and proven.

Keywords

Measurable FunctionsLebesgue IntegrabilityEgorov TheoremLebesgue Limit Theorems
Type
Chapter
Information
Classical and Discrete Functional Analysis with Measure Theory , pp. 97 - 117
Publisher: Cambridge University Press
Print publication year: 2022

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  • Lebesgue Integral
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.005
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  • Lebesgue Integral
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.005
Available formats
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  • Lebesgue Integral
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.005
Available formats
×