English

A formalisation of Gallagher's ergodic theorem

Logic in Computer Science 2023-02-02 v1 Number Theory

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.

Cite

@article{arxiv.2302.00448,
  title  = {A formalisation of Gallagher's ergodic theorem},
  author = {Oliver Nash},
  journal= {arXiv preprint arXiv:2302.00448},
  year   = {2023}
}

Comments

16 pages, 2 figures

R2 v1 2026-06-28T08:29:05.890Z