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Preliminaries

Published online by Cambridge University Press:  06 January 2022

Martin Buntinas
Martin Buntinas
Affiliation:
Loyola University, Chicago
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Summary

This preliminary chapter contains notations, definitions, and basic concepts needed for the study of Measure Theory and Functional Analysis. Most of this chapter is for reference and may be read only as needed. Included are concepts such as Convergence, Continuity, and Compactness in Euclidean Spaces. The theory of Euclidean Measure and sets of Measure Zero are covered. An overview is included of Integration sufficient to begin the study of Functional Analysis. The chapter finishes with topics such as Functions of Bounded Variation, Inequalities, along with a discussion of the Axiom of Choice.

Keywords

PreliminariesNotationsEuclidean SpaceConvergenceContinuityCompactnessInequalitiesBounded VariationMeasure ZeroTopology
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Chapter
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Classical and Discrete Functional Analysis with Measure Theory , pp. 1 - 62
Publisher: Cambridge University Press
Print publication year: 2022

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  • Preliminaries
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.002
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  • Preliminaries
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.002
Available formats
×

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.

  • Preliminaries
  • Martin Buntinas, Loyola University, Chicago
  • Book: Classical and Discrete Functional Analysis with Measure Theory
  • Online publication: 06 January 2022
  • Chapter DOI: https://doi.org/10.1017/9781139524445.002
Available formats
×