A Survey on the Hausdorff Dimension of Intersections

Abstract

Let A and B be Borel subsets of the Euclidean n-space with dimA+dimB>n. This is a survey on the following question: what can we say about the Hausdorff dimension of the intersections A∩(g(B)+z) for generic orthogonal transformations g and translations by z?

Keywords

• Hausdorff dimension
• intersection
• projection
• energy integral
• Fourier transform