Among other results
it is proved that if (X,A,μ) is a probability space, E a Hausdorff locally
convex space such that (E′,σ(E′,E)) contains an increasing sequence of
absolutely convex compact sets with dense union, and f : X → E weakly
measurable with f(X) ⊂ K, a weakly compact convex subset of E, then f is
weakly equivalent to g : X → E with g(X) contained in a separable subset of
K.
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