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Boolean σ-algebras

  • Paul R. Halmos
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Between Boolean algebras and complete Boolean algebras there is room for many intermediate concepts. The most important one is that of a Boolean σ-algebra; this means, by definition, a Boolean algebra in which every countable set has a supremum (and therefore, of course, an infimum). Similarly a field of sets is a σ-field if it is closed under the formation of countable unions (and intersections).

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Copyright information

© Springer-Verlag New York Inc. 1974

Authors and Affiliations

  • Paul R. Halmos
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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