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100   $a20200103d2020      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 14$aThe Dual of L?(X,L,?), Finitely Additive Measures and Weak Convergence $eA Primer /$fby John Toland
205   $a1st ed. 2020.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020.
215   $a1 online resource (104 pages)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
311   $a3-030-34731-1 
327   $a1 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,?) -- 9 L?* when X is a Topological Space -- 10 Reconciling Representations -- References -- Index.
330   $aIn measure theory, a familiar representation theorem due to F. Riesz identifies the dual space Lp(X,L,?)* with Lq(X,L,?), where 1/p+1/q=1, as long as 1 ? p<?. However, L?(X,L,?)* cannot be similarly described, and is instead represented as a class of finitely additive measures. This book provides a reasonably elementary account of the representation theory of L?(X,L,?)*, examining pathologies and paradoxes, and uncovering some surprising consequences. For instance, a necessary and sufficient condition for a bounded sequence in L?(X,L,?) to be weakly convergent, applicable in the one-point compactification of X, is given. With a clear summary of prerequisites, and illustrated by examples including L?(Rn) and the sequence space l?, this book makes possibly unfamiliar material, some of which may be new, accessible to students and researchers in the mathematical sciences.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aMeasure theory
606   $aFunctional analysis
606   $aCalculus of variations
606   $aSequences (Mathematics)
606   $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016
606   $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X
615  0$aMeasure theory.
615  0$aFunctional analysis.
615  0$aCalculus of variations.
615  0$aSequences (Mathematics)
615 14$aMeasure and Integration.
615 24$aFunctional Analysis.
615 24$aCalculus of Variations and Optimal Control; Optimization.
615 24$aSequences, Series, Summability.
676   $a515.43
676   $a515.42
700   $aToland$b John$4aut$4http://id.loc.gov/vocabulary/relators/aut$05790
906   $aBOOK
912   $a9910483467303321
996   $aThe Dual of L?(X,L,?), Finitely Additive Measures and Weak Convergence$92184194
997   $aUNINA