On the translates of a set which meet it in a set of positive measure
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- by James Foran PDF
- Proc. Amer. Math. Soc. 121 (1994), 893-895 Request permission
Abstract:
Given a singular Borel regular measure ${m_a}$ on ${R^n}$ and a Borel subset E of ${R^n}$, it is shown that the set of vectors x for which ${m_a}((E + x) \cap E) > 0$ is of Lebesgue measure 0. This fact is then used to show that subsets of finite, nonzero, Hausdorff s-measure are nonmeasurable sets with respect to any approximating measure $s - {m_\delta }$.References
- C. A. Rogers, Hausdorff measures, Cambridge University Press, London-New York, 1970. MR 0281862
- Stanisław Saks, Theory of the integral, Second revised edition, Dover Publications, Inc., New York, 1964. English translation by L. C. Young; With two additional notes by Stefan Banach. MR 0167578
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 893-895
- MSC: Primary 28A78; Secondary 26A21, 28A05
- DOI: https://doi.org/10.1090/S0002-9939-1994-1195478-X
- MathSciNet review: 1195478