On the dimension of $s$-Nikodým sets

Damian Dąbrowski; Max Goering; Tuomas Orponen

doi:10.4171/jems/1830

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On the dimension of $s$ -Nikodým sets

Damian Dąbrowski
University of Jyväskylä, Finland
Max Goering
University of Jyväskylä, Finland
Tuomas Orponen
University of Jyväskylä, Finland

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Abstract

Let $s \in [0, 1]$ . We show that a Borel set $N \subset R^{2}$ each of whose points is linearly accessible by an $s$ -dimensional family of lines has Hausdorff dimension at most $2 - s$ . This is a sharp bound, due to a construction of A. Máthé.

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Damian Dąbrowski, Max Goering, Tuomas Orponen, On the dimension of $s$ -Nikodým sets. J. Eur. Math. Soc. (2026), published online first

DOI 10.4171/JEMS/1830