Abstract
This chapter is devoted to the set \(\mathfrak G\) of finitely additive measures \(\omega \) which take only the values 0 or 1 and explains the sense in which every essentially bounded function is constant \(\omega \)-almost everywhere. The existence of elements of \(\mathfrak G\) with prescribed properties is established using Zorn’s lemma and a relation between elements of \(\mathfrak G\) and maximal filters. This observation and its consequences dominate subsequent developments.
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Toland, J. (2020). \(\mathfrak G\): 0–1 Finitely Additive Measures. In: The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-34732-1_5
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DOI: https://doi.org/10.1007/978-3-030-34732-1_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-34731-4
Online ISBN: 978-3-030-34732-1
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