# Strictly Positive Measures on Boolean Algebras

Džamonja, M and Plebanek, G (2008) Strictly Positive Measures on Boolean Algebras. Journal of Symbolic Logic, 73 (4). pp. 1416-1432. ISSN 1943-5886

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## Abstract

We investigate strictly positive finitely additive measures on Boolean algebras and strictly positive Radon measures on compact zerodimensional spaces. The motivation is to find a combinatorial characterisation of Boolean algebras which carry a strictly positive finitely additive finite measure with some additional properties, such as separability or nonatomicity. A possible consistent characterisation for an algebra to carry a separable strictly positive measure was suggested by Talagrand in 1980, which is that the Stone space K of the algebra satisfies that its space M(K) of measures is weakly separable, equivalently that C(K) embeds into l8. We show that there is a ZFC example of a Boolean algebra (so of a compact space) which satisfies this condition and does not support a separable strictly positive measure. However, we use this property as a tool in a proof which shows that under MA+\neg CH every atomless ccc Boolean algebra of size <

Item Type: Article Faculty of Science > School of Mathematics Vishal Gautam 18 Mar 2011 10:19 24 Jul 2019 15:03 https://ueaeprints.uea.ac.uk/id/eprint/19963 10.2178/jsl/1230396929