A formalisation of Gallagher's ergodic theorem

Oliver Nash

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arXiv · 2302.00448

A formalisation of Gallagher's ergodic theorem

Oliver Nash

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Abstract

Gallagher's ergodic theorem is a result in metric number theory. It states that the approximation of real numbers by rational numbers obeys a striking 'all or nothing' behaviour. We discuss a formalisation of this result in the Lean theorem prover. As well as being notable in its own right, the result is a key preliminary, required for Koukoulopoulos and Maynard's stunning recent proof of the Duffin-Schaeffer conjecture.

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Oliver Nash. 2023-02-01. A formalisation of Gallagher's ergodic theorem. https://arxiv.org/abs/2302.00448

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