Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes
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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.
Falconer , K & Mattila , P 2016 , ' Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes ' Journal of Fractal Geometry , vol. 3 , no. 4 , pp. 319-329 . DOI: 10.4171/JFG/38
Journal of Fractal Geometry
© 2016, European Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.ems-ph.org/journals / https://doi.org/10.4171/JFG/38
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