A Decomposition of Measures
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 953-959
Voir la notice de l'article provenant de la source Cambridge University Press
Let X be a set, a σ-ring of subsets of X, and let μ be a measure on . Following (1), we define μ to be semifinite if We show (Theorem 1) that every measure can be reduced to a semifinite measure for many practical purposes. In many cases, this reduction can be made even more significantly (Theorems 2 and 3). Finally, necessary and sufficient conditions that a semifinite measure be c-finite are given as a corollary to Theorem 3.
Luther, Norman Y. A Decomposition of Measures. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 953-959. doi: 10.4153/CJM-1968-092-0
@article{10_4153_CJM_1968_092_0,
author = {Luther, Norman Y.},
title = {A {Decomposition} of {Measures}},
journal = {Canadian journal of mathematics},
pages = {953--959},
year = {1968},
volume = {20},
number = {1},
doi = {10.4153/CJM-1968-092-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-092-0/}
}
[1] 1. Berberian, S. K., Measure and integration (Macmillan, New York, 1965). Google Scholar
[2] 2. Halmos, P. R., Measure theory (Van Nostrand, New York, 1950).10.1007/978-1-4684-9440-2 Google Scholar | DOI
[3] 3. Hewitt, E. and Stromberg, K., Real and abstract analysis (Springer-Verlag, New York, 1965). Google Scholar
[4] 4. Johnson, R. A., On the Lebesgue decomposition theorem, Proc. Amer. Math. Soc. 18 (1967), 628–632. Google Scholar
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