Proof of `Birkhoff's pointwise ergodic theorem`
groundedproofs/Lax606786Proofs/ErgodicStatements.lean · lax-606786
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Garsia's maximal ergodic theorem (Garsia 1965; see also Rudolph 1990) gives a weak-type maximal inequality, which extends almost everywhere convergence from the dense set of coboundaries plus invariant functions (von Neumann's splitting, von Neumann 1932) to all of ; ergodicity identifies the limit with the space average.