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The Dual of L∞(X,L,λ), Finitely Addi...
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The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence = A Primer /
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence/ by John Toland.
其他題名:
A Primer /
作者:
Toland, John.
面頁冊數:
X, 99 p. 1 illus.online resource. :
Contained By:
Springer Nature eBook
標題:
Sequences, Series, Summability. -
電子資源:
https://doi.org/10.1007/978-3-030-34732-1
ISBN:
9783030347321
The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence = A Primer /
Toland, John.
The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence
A Primer /[electronic resource] :by John Toland. - 1st ed. 2020. - X, 99 p. 1 illus.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.
1 Introduction -- 2 Notation and Preliminaries -- 3 L∞ and its Dual -- 4 Finitely Additive Measures -- 5 G: 0-1 Finitely Additive Measures -- 6 Integration and Finitely Additive Measures -- 7 Topology on G -- 8 Weak Convergence in L∞(X,L,λ) -- 9 L∞* when X is a Topological Space -- 10 Reconciling Representations -- References -- Index.
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.
ISBN: 9783030347321
Standard No.: 10.1007/978-3-030-34732-1doiSubjects--Topical Terms:
672022
Sequences, Series, Summability.
LC Class. No.: QA312-312.5
Dewey Class. No.: 515.42
The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence = A Primer /
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