A New Estimate for a Problem of Steinhaus
نویسنده
چکیده
Steinhaus asked whether there exists a subset of the plane which, no matter how translated and rotated, always contains exactly one point with integer coordinates. It is still unknown if there exist sets with the Steinhaus property. Using harmonic analysis we prove that if a measurable set S R 2 satisses R S jxj 10 3 + dx < 1, for some > 0, then it cannot have the Steinhaus property. 0. Introduction 0.1 A problem of Steinhaus. Steinhaus 8, problem 59] asked whether there is a planar set S which, no matter how translated and rotated, always contains exactly one point with integer coordinates.
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