The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence A Primer 1st Edition John Toland

The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence A Primer 1st Edition – Ebook Instant Download/Delivery ISBN(s): 9783030347314,3030347311,9783030347321, 303034732X

Product details:

• ISBN-10: 303034732X
• ISBN-13: 9783030347321
• Author: John Toland

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.

Table contents:

1. Introduction
2. Notation and Preliminaries
3. and Its Dual
4. Finitely Additive Measures
5. : 0–1 Finitely Additive Measures
6. Integration and Finitely Additive Measures
7. Topology on
8. Weak Convergence in
9. When X is a Topological Space
10. Reconciling Representations

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