A characterization theorem for L.C.S. valued functions (Q1062164)

A function f is \({\bar \mu}\)-measurable if it is the uniform limit of a net \((f_{\alpha})_{\alpha \in \Lambda}\) of \(\mu\)-measurable functions taking values in a Hausdorff locally convex space. The author generalizes the Pettis theorem for the Bochner measurability by giving necessary and sufficient conditions for f to be \({\bar \mu}\)-measurable. Furthermore, an analogue of Egorov's theorem is deduced.