Year: 2026
Type: preprint
Abstract: We show that there is a $Π^0_2$ subset $B$ of the Euclidean plane, of Hausdorff dimension 1, such that for every line $\ell$ through the origin with hyperarithmetic direction, the projection of $B$ onto $\ell$ has Hausdorff dimension 0, thus is exceptional for Marstrand's projection theorem. It follows that for any computable ordinal $α$, being $α$-random does not guarantee the ``almost-all'' statement of the projection theorem.
Source: arXiv (Cornell University)
Authors: Greenberg, Noam, Turetsky, Daniel
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204583718
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