Hausdorff dimension and projections related to intersections

Abstract

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

The assumptions of Theorems 4.2 and 4.3 have been slightly changed and some other minor changes have been made. Reorganization of some sections and several small changes made