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On consequences of the Banach-Kuratowski theorem for Stone algebra valued measures. (English) Zbl 0676.28005
Assuming the continuum hypothesis, the author proves the following result: Let \(\Omega\) be a set with \(card(\Omega)=c\) and let S be a compact Hausdorff space such that (i) the closure of every open subset of S is open, and (ii) every meagre subset of S is nowhere dense. Then there exists no nonzero \(\sigma\)-finite order continuous submeasure \(\eta\) : 2\({}^{\Omega}\to C(S)\) satisfying \(\eta (\{\omega \})=0\) for all \(\omega\in \Omega\).
Reviewer: Klaus D.Schmidt

MSC:
28B05 Vector-valued set functions, measures and integrals
28B15 Set functions, measures and integrals with values in ordered spaces
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