EXCEPTIONAL SET ESTIMATES FOR THE HAUSDORFF DIMENSION OF INTERSECTIONS

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Mattila , P 2017 , ' EXCEPTIONAL SET ESTIMATES FOR THE HAUSDORFF DIMENSION OF INTERSECTIONS ' , Annales Academiae Scientiarum Fennicae. Mathematica , vol. 42 , no. 2 , pp. 611-620 . https://doi.org/10.5186/aasfm.2017.4236

Title: EXCEPTIONAL SET ESTIMATES FOR THE HAUSDORFF DIMENSION OF INTERSECTIONS
Author: Mattila, Pertti
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2017
Language: eng
Number of pages: 10
Belongs to series: Annales Academiae Scientiarum Fennicae. Mathematica
ISSN: 1239-629X
URI: http://hdl.handle.net/10138/224529
Abstract: Let A and B be Borel subsets of the Euclidean n-space with dim A + dim B > n and let 0 <u <dim A + dim B n where dim denotes Hausdorff dimension. Let E be the set of those orthogonal transformations g is an element of O(n) for which dim A boolean AND (g(B) + z) n + 1, then dim E 2n-1, then dim A boolean AND (B + z) > u for z in a set of positive Lebesgue measure. If dim A + dim B <2n 1, the set of exceptional g is an element of 0(n) has dimension at most n(n-1)/2-u.
Subject: Hausdorff dimension
intersection
energy integral
Fourier transform
FOURIER-TRANSFORMS
PROJECTIONS
CAPACITIES
111 Mathematics
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