Convex Corson compacta and Radon measures

Volume 175 / 2002

Grzegorz Plebanek Fundamenta Mathematicae 175 (2002), 143-154 MSC: Primary 28C15; Secondary 46E27. DOI: 10.4064/fm175-2-4


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.


  • Grzegorz PlebanekInstitute of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland

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