Atomic and nonatomic measures
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- by Roy A. Johnson
- Proc. Amer. Math. Soc. 25 (1970), 650-655
- DOI: https://doi.org/10.1090/S0002-9939-1970-0279266-8
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Abstract:
Elementary properties of atomic and nonatomic measures are investigated. In addition, it is shown that every measure can be written as the sum of a purely atomic measure and a nonatomic measure. Conditions are given under which this decomposition is unique.References
- Sterling K. Berberian, Measure and integration, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1965. MR 0183839
- Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
- Roy A. Johnson, On the lebesgue decomposition theorem, Proc. Amer. Math. Soc. 18 (1967), 628–632. MR 218516, DOI 10.1090/S0002-9939-1967-0218516-0
- J. D. Knowles, On the existence of non-atomic measures, Mathematika 14 (1967), 62–67. MR 214719, DOI 10.1112/S0025579300008020
- Norman Y. Luther, Lebesgue decomposition and weakly Borel measures, Duke Math. J. 35 (1968), 601–615. MR 229780
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 650-655
- MSC: Primary 28.13
- DOI: https://doi.org/10.1090/S0002-9939-1970-0279266-8
- MathSciNet review: 0279266