Pointwise compactness and measurability

Surjit Singh Khurana

Vol. 83 (1979), No. 2, 387–391

DOI: 10.2140/pjm.1979.83.387

Abstract

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.

Mathematical Subject Classification 2000

Primary: 46G10

Secondary: 28A20

Milestones

Received: 12 August 1978

Published: 1 August 1979