$$\mathfrak G$$: 0–1 Finitely Additive Measures

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


This chapter is devoted to the set of finitely additive measures which take only the values 0 or 1 and explains the sense in which every essentially bounded function is constant-almost everywhere. The existence of elements of with prescribed properties is established using Zorn’s lemma and a relation between elements of and maximal filters. This observation and its consequences dominate subsequent developments.

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 pages6
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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