Abstract
We give a short proof of the fact that there are no measurable subsets of Euclidean space (in dimension $d\ge 3$) which, no matter how translated and rotated, always contain exactly one integer lattice point. In dimension $d=2$ (the original Steinhaus problem) the question remains open.
Citation
Mihail N. Kolountzakis. Michael Papadimitrakis. "The Steinhaus tiling problem and the range of certain quadratic forms." Illinois J. Math. 46 (3) 947 - 951, Fall 2002. https://doi.org/10.1215/ijm/1258130994
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