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1 - Lebesgue Measure

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

Outer, Inner, and Lebesgue Measure are defined and systematically studied; first for (n-dimensional) intervals, then for finite and countable union of intervals, then for open and closed sets, and finally for general Lebesgue Measurable sets in Euclidean Spaces. The Approximation Theorem and the Caratheodory Characterization of Measurability are proven. Borel sets are studied and examples are given of Nonmeasurable Sets, as well as Measurable Sets which are not Borel.

Keywords

Outer MeasureInner MeasureLebesgue MeasureApproximation TheoremCaratheodory CharacterizationBorel SetsNonmeasurable Sets
Type
Chapter
Information
Classical and Discrete Functional Analysis with Measure Theory , pp. 65 - 96
Publisher: Cambridge University Press
Print publication year: 2022

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  • Lebesgue Measure
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.004
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  • Lebesgue Measure
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.004
Available formats
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  • Lebesgue Measure
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.004
Available formats
×