SWhat changed
Proved the historical pointwise ergodic theorem for the paper's flow setting.
Scientific scope
The record is Birkhoff's sole-author 1931 PNAS paper. It does not absorb von Neumann's mean ergodic theorem, Hopf's proof and extensions, later abstract formulations or an unconditional identification of time and phase averages without ergodicity assumptions.
Evidence
The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is Birkhoff's sole-author 1931 PNAS paper. It does not absorb von Neumann's mean ergodic theorem, Hopf's proof and extensions, later abstract formulations or an unconditional identification of time and phase averages without ergodicity assumptions.
Contributors
- George D. Birkhoff · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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