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

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<∞. 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 suffici