Series convergence on boolean algebras
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- by Miloslav Nosal PDF
- Proc. Amer. Math. Soc. 29 (1971), 211-212 Request permission
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
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C. Carathéodory, Algebraic theory of measure and integration, Chelsea, New York, 1963. MR 26 #6340.
- Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
- Paul R. Halmos, Lectures on Boolean algebras, Van Nostrand Mathematical Studies, No. 1, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. MR 0167440 R. Sikorski, Boolean algebras, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 25, Springer-Verlag, Berlin, 1969. MR 39 #4053.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 211-212
- MSC: Primary 06.60
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276152-5
- MathSciNet review: 0276152