Atomic and nonatomic measures
Author:
Roy A. Johnson
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
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Abstract | References | Similar Articles | Additional Information
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.
- Sterling K. Berberian, Measure and integration, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1965. MR 0183839
- Paul R. Halmos, Measure Theory, D. Van Nostrand Company, 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 https://doi.org/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 https://doi.org/10.1112/S0025579300008020
- Norman Y. Luther, Lebesgue decomposition and weakly Borel measures, Duke Math. J. 35 (1968), 601–615. MR 229780
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Keywords:
Atom,
purely atomic measure,
atomic measure,
nonatomic measure,
sigma-finite measure,
semifinite measure
Article copyright:
© Copyright 1970
American Mathematical Society