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• W2103291852 abstract "Let D be a compact set in the plane, t a real number, and D t the linear set { x + ty|x + iy e D }. We are interested in the Hausdorff dimensions of D and D t , and assume that dim D = d ≤ 1. A number t is “exceptional” if dim D t ; the exceptional numbers form a Borel set of d-dimensional measure zero [3]. (Marstrand [4, p. 268] proves a similar conclusion for the Lebesgue measure of the exceptional set.) In this note we exhibit a planar set D of Hausdorff dimension d and a linear set E for which dim D t ≤ r for every t in E , but dim E > 0. The method does not come very close to the probable truth, that the set E can have dimension r . But perhaps the result can be improved by more subtle calculation, for example, as in Jarnik [2]." @default.
• W2103291852 created "2016-06-24" @default.
• W2103291852 creator A5022824554 @default.
• W2103291852 date "1969-06-01" @default.
• W2103291852 modified "2023-09-25" @default.
• W2103291852 title "An exceptional set for Hausdorff dimension" @default.
• W2103291852 cites W2120045167 @default.
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• W2103291852 doi "https://doi.org/10.1112/s0025579300004617" @default.
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