What is recorded here?
Proved almost-everywhere convergence of time averages for the measure-preserving dynamical setting stated in the paper, yielding the pointwise ergodic theorem in that framework.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
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.
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People and systems
George D. Birkhoff
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Documented countries / regions: United States
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English catalogue narrative
Birkhoff: proof of the ergodic theorem
Proved almost-everywhere convergence of time averages for the measure-preserving dynamical setting stated in the paper, yielding the pointwise ergodic theorem in that framework.
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.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
George D. Birkhoff
The named authors contributed to this scoped work; individual effort shares and later applications are not assigned by the byline.