The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence

A Primer

von John Toland

99 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: SpringerBriefs in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Mathematische Analysis, allgemein Integralrechnung und -gleichungen
• ISBN: 9783030347314
• Sprache: Englisch
• Erscheinungsdatum: 07.02.2020
• Größe: 23.5 x 15.5 cm
• Verlag: Springer International Publishing