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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
In measure theory, a familiar representation theorem due to F. Riesz identifies the dual space Lp(X,L,λ)* with Lq(X,L,λ), where 1/p+1/q=1, as long as 1 ≤ p<∞. However, L∞(X,L,λ)* cannot be similarly described, and is instead represented as a class of finitely additive measures.
This book provides a reasonably elementary account of the representation theory of L∞(X,L,λ)*, examining pathologies and paradoxes, and uncovering some surprising consequences. For instance, a necessary and sufficient condition for a bounded sequence in L∞(X,L,λ) to be weakly convergent, applicable in the one-point compactification of X, is given.
With a clear summary of prerequisites, and illustrated by examples including L∞(Rn) and the sequence space l∞, this book makes possibly unfamiliar material, some of which may be new, accessible to students and researchers in the mathematical sciences.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence
Book Subtitle: A Primer
Authors: John Toland
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-030-34732-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-34731-4Published: 07 February 2020
eBook ISBN: 978-3-030-34732-1Published: 03 January 2020
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: X, 99
Number of Illustrations: 1 b/w illustrations
Topics: Measure and Integration, Functional Analysis, Calculus of Variations and Optimal Control; Optimization, Sequences, Series, Summability