The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence [[electronic resource] ] : A Primer / / by John Toland
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| Autore: |
Toland John
|
| Titolo: |
The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence [[electronic resource] ] : A Primer / / by John Toland
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Edizione: | 1st ed. 2020. |
| Descrizione fisica: | 1 online resource (104 pages) |
| Disciplina: | 515.43 |
| 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 |
| ISBN: | 3-030-34732-X |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 996418191803316 |
| Lo trovi qui: | Univ. di Salerno |
| Opac: | Controlla la disponibilità qui |
Serie:
SpringerBriefs in Mathematics, . 2191-8198