## Measures on compact HS spaces

### Volume 143 / 1993

Fundamenta Mathematicae 143 (1993), 41-54
DOI: 10.4064/fm-143-1-41-54

#### Abstract

We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomorphic to the measure algebra of $2^{ω_1}$. The first construction uses ♢ to produce an S-space with no convergent sequences in which every perfect set is a $G_δ$. A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The second space is constructed under CH and is both HS and HL.