On the translates of a set which meet it in a set of positive measure
Abstract: Given a singular Borel regular measure on and a Borel subset E of , it is shown that the set of vectors x for which 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 .
-  C. A. Rogers, Hausdorff measures, Cambridge University Press, London-New York, 1970. MR 0281862
-  Stanisław Saks, Theory of the integral, Second revised edition. English translation by L. C. Young. With two additional notes by Stefan Banach, Dover Publications, Inc., New York, 1964. MR 0167578
Keywords: Borel regular measure, Hausdorff s-dimensional measure
Article copyright: © Copyright 1994 American Mathematical Society