Convex Corson compacta and Radon measures

Grzegorz Plebanek¹

¹ Institute of Mathematics University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland

Fundamenta Mathematicae, Tome 175 (2002) no. 2, pp. 143-154.

Résumé

Assuming the continuum hypothesis, we show that (i) there is a compact convex subset $L$ of $\Sigma ({\mathbb{R}}^{{\omega }_1})$, and a probability Radon measure on $L$ which has no separable support; (ii) there is a Corson compact space $K$, and a convex weak${}^{\ast }$-compact set $M$ of Radon probability measures on $K$ which has no $G_{\delta }$-points.

Détail

DOI : 10.4064/fm175-2-4

Mots-clés : assuming continuum hypothesis there compact convex subset mit sigma mathbb omega probability radon measure which has separable support there corson compact space convex weak * compact set radon probability measures which has delta points