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The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence : A Primer / by John Toland
(SpringerBriefs in Mathematics. ISSN:21918201)
Edition | 1st ed. 2020. |
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Publisher | (Cham : Springer International Publishing : Imprint: Springer) |
Year | 2020 |
Size | X, 99 p. 1 illus : online resource |
Authors | *Toland, John author SpringerLink (Online service) |
Subjects | LCSH:Measure theory LCSH:Functional analysis LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Sequences (Mathematics) FREE:Measure and Integration FREE:Functional Analysis FREE:Calculus of Variations and Optimization FREE:Sequences, Series, Summability |
Notes | 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 HTTP:URL=https://doi.org/10.1007/978-3-030-34732-1 |
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E-Book | Location | Media type | Volume | Call No. | Status | Reserve | Comments | ISBN | Printed | Restriction | Designated Book | Barcode No. |
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E-Book | オンライン | 電子ブック |
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Springer eBooks | 9783030347321 |
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電子リソース |
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EB00196676 |
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Material Type | E-Book |
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Classification | LCC:QA312-312.5 DC23:515.42 |
ID | 4000134723 |
ISBN | 9783030347321 |
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