Constancy results for special families of projections
Classical Analysis and ODEs
2013-10-07 v2
Abstract
Let {\mathbb{V} = V x R^l : V \in G(n-l,m-l)} be the family of m-dimensional subspaces of R^n containing {0} x R^l, and let \pi_{\mathbb{V}} : R^n --> \mathbb{V} be the orthogonal projection onto \mathbb{V}. We prove that the mapping V \mapsto Dim \pi_{\mathbb{V}}(B) is almost surely constant for any analytic set B \subset R^n, where Dim denotes either Hausdorff or packing dimension.
Keywords
Cite
@article{arxiv.1208.1876,
title = {Constancy results for special families of projections},
author = {Katrin Fässler and Tuomas Orponen},
journal= {arXiv preprint arXiv:1208.1876},
year = {2013}
}
Comments
22 pages. v2: corrected typos and improved readability throughout the paper, to appear in Math. Proc. Cambridge Philos. Soc