A duality principle
HTML articles powered by AMS MathViewer
- by Wolfgang Sander PDF
- Proc. Amer. Math. Soc. 84 (1982), 609-610 Request permission
Abstract:
With the aid of the Baire category theory we prove an extension of Erdös’ well-known duality principle concerning sets of Lebesgue measure zero and sets of first category.References
-
P. Cholewa, Sierpiński-Erdös duality principle in the abstract Baire-category theory, manuscript.
- P. Erdös, Some remarks on set theory, Ann. of Math. (2) 44 (1943), 643–646. MR 9614, DOI 10.2307/1969101
- John C. Morgan II, On translation invariant families of sets, Colloq. Math. 34 (1975/76), no. 1, 63–68. MR 404589, DOI 10.4064/cm-34-1-63-68
- John C. Morgan II, The absolute Baire property, Pacific J. Math. 65 (1976), no. 2, 421–436. MR 425930
- John C. Morgan II, Baire category from an abstract viewpoint, Fund. Math. 94 (1977), no. 1, 13–23. MR 433416, DOI 10.4064/fm-94-1-59-64
- John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443
- C. A. Rogers, Hausdorff measures, Cambridge University Press, London-New York, 1970. MR 0281862
- Wolfgang Sander, A decomposition theorem, Proc. Amer. Math. Soc. 83 (1981), no. 3, 553–554. MR 627689, DOI 10.1090/S0002-9939-1981-0627689-4 W. Sierpiński, Sur la dualité entre la première catégorie et la mesure nulle, Fund. Math. 1 (1920), 105-111.
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 609-610
- MSC: Primary 54E52; Secondary 28A05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0643759-X
- MathSciNet review: 643759