# 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} }

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 \begin{equation} \[{\dim _{\text{H}}}{\pi _e}(K) = \min \{ {\dim _{\text{H}}}{\text{ }}K{\text{, 1}}\} \] \end{equation} for almost every \[e \in…

## 5 Citations

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