1994•Proceedings of the American Mathematical SocietyRequires access
On the Translates of a Set which Meet it in a Set of Positive Measure
James M. Foran
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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 $s - {m_\delta }$.