A generalization of Lusin’s theorem
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- by Michael L. Wage
- Proc. Amer. Math. Soc. 52 (1975), 327-332
- DOI: https://doi.org/10.1090/S0002-9939-1975-0379782-9
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Abstract:
In this note we characterize $\sigma$-finite Riesz measures that allow one to approximate measurable functions by continuous functions in the sense of Lusin’s theorem. We call such measures Lusin measures and show that not all $\sigma$-finite measures are Lusin measures. It is shown that if a topological space $X$ is either normal or countably paracompact, then every measure on $X$ is a Lusin measure. A counterexample is given to show that these sufficient conditions are not necessary.References
- C. H. Dowker, On countably paracompact spaces, Canad. J. Math. 3 (1951), 219–224. MR 43446, DOI 10.4153/cjm-1951-026-2
- J. L. Kelley, Measures on Boolean algebras, Pacific J. Math. 9 (1959), 1165–1177. MR 108570, DOI 10.2140/pjm.1959.9.1165
- D. J. Hebert and H. Elton Lacey, On supports of regular Borel measures, Pacific J. Math. 27 (1968), 101–118. MR 235088, DOI 10.2140/pjm.1968.27.101
- Mary Ellen Rudin, A normal space $X$ for which $X\times I$ is not normal, Fund. Math. 73 (1971/72), no. 2, 179–186. MR 293583, DOI 10.4064/fm-73-2-179-186
- Mary Ellen Rudin, Souslin’s conjecture, Amer. Math. Monthly 76 (1969), 1113–1119. MR 270322, DOI 10.2307/2317183
- Stephen Willard, General topology, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970. MR 0264581
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 327-332
- MSC: Primary 28A10
- DOI: https://doi.org/10.1090/S0002-9939-1975-0379782-9
- MathSciNet review: 0379782