Integration and Finitely Additive Measures

Research output: Chapter or section in a book/report/conference proceedingChapter or section


This chapter deals with the integration of essentially bounded measurable functions with respect to finitely additive measures like those that featured in the Yosida–Hewitt representation theorem in Chap. 3. The chapter includes a study of integration of an essentially bounded function u with respect to elements of, which leads to the multivalued essential range of u, and ends with an example of finitely additive measures that are not countably additive, but which coincide with Lebesgue measure when integrating continuous functions.

Original languageEnglish
Title of host publicationThe Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence
Place of PublicationCham, Switzerland
PublisherSpringer Science and Business Media B.V.
Number of pages10
ISBN (Electronic)9783030347321
ISBN (Print)9783030347314
Publication statusE-pub ahead of print - 3 Jan 2020

Publication series

NameSpringerBriefs in Mathematics
ISSN (Print)2191-8198
ISSN (Electronic)2191-8201

Bibliographical note

Publisher Copyright:
© 2020, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Copyright 2021 Elsevier B.V., All rights reserved.

ASJC Scopus subject areas

  • General Mathematics


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