Lax Lean Archive

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Proof of `The maximal ergodic theorem` (1st statement)

groundedproofs/Lax606786Proofs/Birkhoff/Maximal.lean · lax-606786

What this proof establishes

no assumptions

thm✓Lax606786.MaximalErgodicTheorem (1st statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitLab

Description

Garsia's proof (Garsia 1965), run on the recursion Fn+1=max(0,f+Fn∘σ)Fₙ₊₁ = max(0, f + Fₙ ∘ σ) for the maximal Birkhoff sum.