Convex Corson compacta and Radon measures
Volume 175 / 2002
Fundamenta Mathematicae 175 (2002), 143-154
MSC: Primary 28C15; Secondary 46E27.
DOI: 10.4064/fm175-2-4
Abstract
Assuming the continuum hypothesis, we show that
(i) there is a compact convex subset $L$ of ${\mit \Sigma }({{\mathbb R}}^{\omega _{1}})$, and a probability Radon measure on $L$ which has no separable support;
(ii) there is a Corson compact space $K$, and a convex weak$^*$-compact set $M$ of Radon probability measures on $K$ which has no $G_{\delta }$-points.
