Strictly positive measures on Boolean algebras

Džamonja, Mirna and Plebanek, Grzegorz (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 \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 10:19
Last Modified:	13 Oct 2025 03:31
URI:	https://ueaeprints.uea.ac.uk/id/eprint/19963
DOI:	10.2178/jsl/1230396929

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