Papers › A formalisation of Gallagher's ergodic theorem

A formalisation of Gallagher's ergodic theorem

1 Feb 2023arXiv:2302.00448links table onlyarchive 2025-07-28

Oliver Nash

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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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