Hausdorff dimension and projections related to intersections

Pertti Mattila

Hausdorff dimension and projections related to intersections

Classical Analysis and ODEs 2020-09-28 v3

Authors: Pertti Mattila

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.

Keywords

hausdorff dimension hausdorff measure and dimension

Cite

@article{arxiv.2005.04947,
  title  = {Hausdorff dimension and projections related to intersections},
  author = {Pertti Mattila},
  journal= {arXiv preprint arXiv:2005.04947},
  year   = {2020}
}

Comments

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

Hausdorff dimension and projections related to intersections

Abstract

Keywords

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