Hausdorff dimension and capacities of intersections of sets in n-space (Q796675)

Let A and B be Borel sets in \(R^ n\). One of the basic questions studied is under what conditions \(\dim A\cap fB=\dim A+\dim B-n\) or \(\dim A\cap fB\geq \dim A+\dim B-n\) for ''many'' isometries or similarities f. Here dim denotes Hausdorff dimension. Similarly, several relations between the capacities \(C_ s(A)\), \(C_ t(B)\) and \(C_{s+t-n}(A\cap fB)\) are proven.