Weakly compact sets in L∞(μ,E)

Using the theory of liftings, we give simple new proofs of the characterizations of the relatively weakly compact subsets and weak Cauchy sequences of L∞(E). Also a different proof, of a deep result of J. Diestel, W. Ruess, W. Schachermayer about weak compactness in L1(E), is given. © 2012 Elsevier Inc. All rights reserved