Hausdorff dimension of intersections with planes and general sets

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Mattila , P 2021 , ' Hausdorff dimension of intersections with planes and general sets ' , Journal of Fractal Geometry , vol. 8 , no. 4 , pp. 389-401 . https://doi.org/10.4171/JFG/110

Title: Hausdorff dimension of intersections with planes and general sets
Author: Mattila, Pertti
Other contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2021-09-29
Language: eng
Number of pages: 13
Belongs to series: Journal of Fractal Geometry
ISSN: 2308-1309
DOI: https://doi.org/10.4171/JFG/110
URI: http://hdl.handle.net/10138/335639
Abstract: We give conditions on a general family P-lambda : R-n -> R-m, lambda is an element of Lambda of orthogonal projections which guarantee that the Hausdorff dimension formula dim A boolean AND P-lambda(-1){u} = s - m holds generically for measurable sets A subset of R-n with positive and finite s-dimensional Hausdorff measure, s > m, and with positive lower density. As an application we prove for measurable sets A, B subset of R-n with positive s- and t-dimensional measures, and with positive lower density that if s + (n - 1)t/n > n, then dim A boolean AND (g(B) + z) = s + t - n for almost all rotations g and for positively many z is an element of R-n.
Subject: Hausdorff dimension
projection
intersection
EXCEPTIONAL SET
PROJECTIONS
CAPACITIES
111 Mathematics
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