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Topological Boolean rings of first and second category. Separating points for a countable family of measures. (English) Zbl 0596.28015
Summary: Topological Boolean rings (Ṟ,u) of first and second category are studied. For example: if Ṟ is $$\sigma$$-complete then (Ṟ,u) is a Baire space if u is generated by a family of $$\sigma$$-subadditive submeasures or by a group-valued measure. It is proved that every countable family of continuous group valued measures on a $$\sigma$$-ring admits separating points. Replacing measures by contents, counterexamples are obtained which imply a previous result of T. E. Armstrong and K. Prikry [Pac. J. Math. 99, 249-264 (1982; Zbl 0489.28006)].

##### MSC:
 28B10 Group- or semigroup-valued set functions, measures and integrals 28A60 Measures on Boolean rings, measure algebras 54H10 Topological representations of algebraic systems