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A decomposition theorem
Author:
Wolfgang Sander
Journal:
Proc. Amer. Math. Soc. 83 (1981), 553-554
MSC:
Primary 28C10; Secondary 54E52
MathSciNet review:
627689
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Abstract: We prove a generalization of the following well-known theorem: " is the disjoint union of a set of first category and a set of Lebesgue measure zero."
- [1]
E. Hewitt and K. A. Ross, Abstract harmonic analysis, Vol. 1, Springer, Berlin, 1963.
- [2]
John
C. Morgan II, On translation invariant families of sets,
Colloq. Math. 34 (1975/76), no. 1, 63–68. MR 0404589
(53 #8389)
- [3]
John
C. Morgan II, The absolute Baire property, Pacific J. Math.
65 (1976), no. 2, 421–436. MR 0425930
(54 #13880)
- [4]
John
C. Morgan II, Baire category from an abstract viewpoint, Fund.
Math. 94 (1977), no. 1, 13–23. MR 0433416
(55 #6392)
- [5]
John
C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in
Mathematics, vol. 2, Springer-Verlag, New York, 1980. A survey of the
analogies between topological and measure spaces. MR 584443
(81j:28003)
- [1]
- E. Hewitt and K. A. Ross, Abstract harmonic analysis, Vol. 1, Springer, Berlin, 1963.
- [2]
- J. C. Morgan II, On translation invariant families of sets, Colloq. Math. 34 (1975), 63-68. MR 0404589 (53:8389)
- [3]
- -, The absolute Baire property, Pacific J. Math. 65 (1976), 421-436. MR 0425930 (54:13880)
- [4]
- -, Baire category from an abstract viewpoint, Fund. Math. 94 (1977), 13-23. MR 0433416 (55:6392)
- [5]
- J. C. Oxtoby, Measure and category, Springer-Verlag, Berlin and New York, 1971. MR 584443 (81j:28003)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1981-0627689-4
PII:
S 0002-9939(1981)0627689-4
Keywords:
Sets of first category,
sets of Lebesgue measure zero,
Baire category from an abstract viewpoint
Article copyright:
© Copyright 1981 American Mathematical Society
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