Hausdorff dimension and projections related to intersections

Abstract

For $S_g(x,y)=x-g(y)$, $x,y\in {ℝ}^n$, $g\in O(n)$, we investigate the Lebesgue measure and Hausdorff dimension of $S_g(A)$ given the dimension of $A$, both for general Borel subsets of ${ℝ}^{2n}$ and for product sets.