The Dual of L (X,L, ), Finitely Additive Measures and Weak Convergence
A Primer
(Sprache: Englisch)
In 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...
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Klappentext zu „The Dual of L (X,L, ), Finitely Additive Measures and Weak Convergence “
In 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.
Inhaltsverzeichnis zu „The Dual of L (X,L, ), Finitely Additive Measures and Weak Convergence “
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, ).- 9 L * when X is a Topological Space.- 10 Reconciling Representations.- References.- Index.
Autoren-Porträt von John Toland
John Toland FRS is a mathematical analyst who worked in nonlinear partial differential equations and served as Director of the Isaac Newton Institute for Mathematical Sciences in Cambridge (2011-2016). He was awarded the London Mathematical Society Berwick Prize (2000) and the Royal Society Sylvester Medal (2012).
Bibliographische Angaben
- Autor: John Toland
- 2020, 1st ed. 2020, X, 99 Seiten, Maße: 15,6 x 0,9 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3030347311
- ISBN-13: 9783030347314
Sprache:
Englisch
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