Combinatorial proofs of two theorems of Lutz and Stull

02/05/2020

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by   Tuomas Orponen, et al.

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The purpose of this note is to give combinatorial-geometric proofs for two Marstrand-type projection theorems for arbitrary, possibly non-analytic, sets, originally due to Lutz and Stull. The original proofs were based on algorithmic information theory, and the notion of pointwise dimension. In this note, the proofs instead rely on δ-discretised variants of a standard "potential theoretic" argument, and the pigeonhole principle.