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The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence : A Primer / / by John Toland



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Autore: Toland John Visualizza persona
Titolo: The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence : A Primer / / by John Toland Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020
Edizione: 1st ed. 2020.
Descrizione fisica: 1 online resource (104 pages)
Disciplina: 515.43
515.42
Soggetto topico: Measure theory
Functional analysis
Calculus of variations
Sequences (Mathematics)
Measure and Integration
Functional Analysis
Calculus of Variations and Optimal Control; Optimization
Sequences, Series, Summability
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence  Visualizza cluster
ISBN: 3-030-34732-X
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910483467303321
Lo trovi qui: Univ. Federico II
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Serie: SpringerBriefs in Mathematics, . 2191-8198