Combinatorial proofs of two theorems of Lutz and Stull

  title={Combinatorial proofs of two theorems of Lutz and Stull},
  author={Tuomas Orponen},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  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 \begin{equation} \[{\dim _{\text{H}}}{\pi _e}(K) = \min \{ {\dim _{\text{H}}}{\text{ }}K{\text{, 1}}\} \] \end{equation} for almost every \[e \in… 
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