Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes

Kenneth Falconer, Pertti Mattila

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Sammanfattning

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.
Originalspråkengelska
TidskriftJournal of Fractal Geometry
Volym3
Nummer4
Sidor (från-till)319-329
Antal sidor11
ISSN2308-1309
DOI
StatusPublicerad - 2016
MoE-publikationstypA1 Tidskriftsartikel-refererad

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  • 111 Matematik

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