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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© 1974 Springer-Verlag New York Inc.
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Halmos, P.R. (1974). Boolean σ-algebras. In: Lectures on Boolean Algebras. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9855-7_13
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DOI: https://doi.org/10.1007/978-1-4612-9855-7_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90094-0
Online ISBN: 978-1-4612-9855-7
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