Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:pointwise_ergodic_theorem
|
| gptkbp:appliesTo |
integrable functions
measure-preserving transformations |
| gptkbp:field |
dynamical systems
ergodic theory measure theory |
| gptkbp:formedBy |
gptkb:George_David_Birkhoff
|
| https://www.w3.org/2000/01/rdf-schema#label |
Birkhoff’s ergodic theorem
|
| gptkbp:implies |
gptkb:ergodic_hypothesis
|
| gptkbp:importantFor |
fundamental result in ergodic theory
|
| gptkbp:relatedTo |
gptkb:von_Neumann_mean_ergodic_theorem
|
| gptkbp:state |
For a measure-preserving transformation, the time average of a function along orbits converges almost everywhere to the space average.
|
| gptkbp:usedIn |
gptkb:probability_theory
gptkb:statistical_mechanics dynamical systems |
| gptkbp:yearProposed |
1931
|
| gptkbp:bfsParent |
gptkb:Kingman’s_subadditive_ergodic_theorem
|
| gptkbp:bfsLayer |
6
|