Measure algebras

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


A measure on a Boolean algebra A is a non-negative real-valued function μ on A such that whenever {p n } is a disjoint sequence of elements of A with a supremum p in A, then \(\mu \left( p \right) = \sum\nolimits_{n} {\mu \left( {{p_{n}}} \right)}\).The principal condition that this definition imposes is called countable additivity, so that a measure can be described as a non-negative and countably additive function on a Boolean algebra.


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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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