Type: Article
Publication Date: 2016-12-22
Citations: 18
DOI: https://doi.org/10.4171/jfg/38
We present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s -dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0 , such that the projection onto any line with direction outside X , of any subset F of E of positive s -dimensional measure, has Hausdorff dimension min{1, s }, i.e. the set of exceptional directions is independent of F . Using duality this leads to results on the dimension of sets that intersect families of lines or hyperplanes in positive Lebesgue measure.