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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Series convergence on boolean algebras

Author: Miloslav Nosal
Journal: Proc. Amer. Math. Soc. 29 (1971), 211-212
MSC: Primary 06.60
MathSciNet review: 0276152
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Abstract: Necessary and sufficient conditions for convergence of an infinite series $ \sum\nolimits_{n = 1}^\infty {{a_n}} $ of elements of an abstract boolean $ \sigma $-algebra is that $ {\lim _{n \to \infty }}{a_n} = 0$.

References [Enhancements On Off] (What's this?)

  • [1] C. Carathéodory, Algebraic theory of measure and integration, Chelsea, New York, 1963. MR 26 #6340.
  • [2] Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950. MR 0033869
  • [3] Paul R. Halmos, Lectures on Boolean algebras, Van Nostrand Mathematical Studies, No. 1, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. MR 0167440
  • [4] R. Sikorski, Boolean algebras, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 25, Springer-Verlag, Berlin, 1969. MR 39 #4053.

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Keywords: Boolean rings, boolean algebras, convergence on boolean algebras, infinite series, series convergence
Article copyright: © Copyright 1971 American Mathematical Society