The Dual of L?(X,L,?), Finitely Additive Measures and Weak Convergence: A Primer

In measure theory, a familiar representation theorem due to F. Riesz identifies the dual space L_p(X,L,λ)* with L_q(X,L,λ), where 1/p+1/q=1, as long as 1 ≤ p 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 f...