Click Here to Download: https://ouo.io/UUW2yXH The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence A Primer By: John Toland Publisher: Springer Print ISBN: 9783030347314, 3030347311 eText ISBN: 9783030347321, 303034732X Copyright year: 2020 Format: EPUB Available from $ 59.99 USD SKU 9783030347321 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.
