00988nam a2200253 i 4500991002930939707536071011s2006 de b 001 0 ger d3534157664b1360434x-39ule_instDip.to Studi Giuridiciita870.9001 Gall, Dorothee183775Die Literatur in der Zeit des Augustus /Dorothee GallDarmstadt :Wissenschaftliche Buchgesellschaft,c2006vi, 184 p. ;24 cmKlassische Philologie kompaktInclude riferimenti bibliografici (p. 168-179) e indice Letteratura latinaStoriaSec. 1. a.C.-1..b1360434x11-10-0711-10-07991002930939707536LE027 R-XV/E 35a12027000134526le027-E25.00-l- 00000.i1457859111-10-07Literatur in der Zeit des Augustus1215909UNISALENTOle02711-10-07ma -gerde 4003541nam 22005895 450 991048346730332120200705113858.03-030-34732-X10.1007/978-3-030-34732-1(CKB)4940000000158921(MiAaPQ)EBC6005430(DE-He213)978-3-030-34732-1(PPN)242846300(EXLCZ)99494000000015892120200103d2020 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence A Primer /by John Toland1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (104 pages)SpringerBriefs in Mathematics,2191-81983-030-34731-1 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.SpringerBriefs in Mathematics,2191-8198Measure theoryFunctional analysisCalculus of variationsSequences (Mathematics)Measure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Calculus of Variations and Optimal Control; Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26016Sequences, Series, Summabilityhttps://scigraph.springernature.com/ontologies/product-market-codes/M1218XMeasure theory.Functional analysis.Calculus of variations.Sequences (Mathematics)Measure and Integration.Functional Analysis.Calculus of Variations and Optimal Control; Optimization.Sequences, Series, Summability.515.43515.42Toland Johnauthttp://id.loc.gov/vocabulary/relators/aut5790BOOK9910483467303321The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence2184194UNINA