# Combinatorial proofs of two theorems of Lutz and Stull

@article{Orponen2021CombinatorialPO,
title={Combinatorial proofs of two theorems of Lutz and Stull},
author={Tuomas Orponen},
journal={Mathematical Proceedings of the Cambridge Philosophical Society},
year={2021},
volume={171},
pages={503 - 514}
}
• Tuomas Orponen
• Published 5 February 2020
• Mathematics
• Mathematical Proceedings of the Cambridge Philosophical Society
Abstract Recently, Lutz and Stull used methods from algorithmic information theory to prove two new Marstrand-type projection theorems, concerning subsets of Euclidean space which are not assumed to be Borel, or even analytic. One of the theorems states that if $K \subset {\mathbb{R}^n}$ is any set with equal Hausdorff and packing dimensions, then $$${\dim _{\text{H}}}{\pi _e}(K) = \min \{ {\dim _{\text{H}}}{\text{ }}K{\text{, 1}}\}$$$ for almost every \[e \in…
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