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JSYML
2008

Strictly positive measures on Boolean algebras

13 years 10 months ago
Strictly positive measures on Boolean algebras
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 l . 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 +
Mirna Dzamonja, Grzegorz Plebanek
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where JSYML
Authors Mirna Dzamonja, Grzegorz Plebanek
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