Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Birkhoff_ergodic_theorem
|
| gptkbp:appliesTo |
measure-preserving transformation
integrable function |
| gptkbp:field |
dynamical systems
ergodic theory measure theory |
| gptkbp:generalizes |
gptkb:strong_law_of_large_numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
pointwise ergodic theorem
|
| gptkbp:namedAfter |
gptkb:George_David_Birkhoff
|
| gptkbp:relatedTo |
gptkb:ergodic_hypothesis
gptkb:mean_ergodic_theorem |
| gptkbp:state |
For a measure-preserving transformation T on a probability space, the time average of an integrable function converges almost everywhere to the space average.
|
| gptkbp:usedIn |
gptkb:probability_theory
gptkb:statistical_mechanics functional analysis |
| gptkbp:yearProved |
1931
|
| gptkbp:bfsParent |
gptkb:Birkhoff's_ergodic_theorem
|
| gptkbp:bfsLayer |
6
|