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- Kolmogorov_automorphism abstract "In mathematics, a Kolmogorov automorphism, K-automorphism, K-shift or K-system is an invertible, measure-preserving automorphism defined on a standard probability space that obeys Kolmogorov's zero-one law. All Bernoulli automorphisms are K-automorphisms (one says they have the K-property), but not vice versa. Many ergodic dynamical systems have been shown to have the K-property, although more recent research has shown that many of these are in fact Bernoulli automorphisms.Although the definition of the K-property seems reasonably general, it stands in sharp distinction to the Bernoulli automorphism. In particular, the Ornstein isomorphism theorem does not apply to K-systems, and so the entropy is not sufficient to classify such systems – there exist uncountably many non-isomorphic K-systems with the same entropy. In essence, the collection of K-systems is large, messy and uncategorized; whereas the B-automorphisms are 'completely' described by Ornstein theory.".
- Kolmogorov_automorphism wikiPageExternalLink S0002-9947-99-02446-0.
- Kolmogorov_automorphism wikiPageID "36563911".
- Kolmogorov_automorphism wikiPageLength "2680".
- Kolmogorov_automorphism wikiPageOutDegree "21".
- Kolmogorov_automorphism wikiPageRevisionID "641097468".
- Kolmogorov_automorphism wikiPageWikiLink Almost_everywhere.
- Kolmogorov_automorphism wikiPageWikiLink Automorphism.
- Kolmogorov_automorphism wikiPageWikiLink Bernoulli_scheme.
- Kolmogorov_automorphism wikiPageWikiLink Category:Ergodic_theory.
- Kolmogorov_automorphism wikiPageWikiLink Dynamical_system.
- Kolmogorov_automorphism wikiPageWikiLink Ergodicity.
- Kolmogorov_automorphism wikiPageWikiLink Intersection_(set_theory).
- Kolmogorov_automorphism wikiPageWikiLink Join_(sigma_algebra).
- Kolmogorov_automorphism wikiPageWikiLink Kolmogorovs_zeroxe2x80x93one_law.
- Kolmogorov_automorphism wikiPageWikiLink Mathematics.
- Kolmogorov_automorphism wikiPageWikiLink Measure-preserving_dynamical_system.
- Kolmogorov_automorphism wikiPageWikiLink Mixing_(mathematics).
- Kolmogorov_automorphism wikiPageWikiLink Null_set.
- Kolmogorov_automorphism wikiPageWikiLink Ornstein_isomorphism_theorem.
- Kolmogorov_automorphism wikiPageWikiLink Sigma-algebra.
- Kolmogorov_automorphism wikiPageWikiLink Standard_probability_space.
- Kolmogorov_automorphism wikiPageWikiLinkText "K-system".
- Kolmogorov_automorphism wikiPageWikiLinkText "Kolmogorov automorphism".
- Kolmogorov_automorphism wikiPageUsesTemplate Template:Reflist.
- Kolmogorov_automorphism subject Category:Ergodic_theory.
- Kolmogorov_automorphism hypernym Automorphism.
- Kolmogorov_automorphism type Process.
- Kolmogorov_automorphism comment "In mathematics, a Kolmogorov automorphism, K-automorphism, K-shift or K-system is an invertible, measure-preserving automorphism defined on a standard probability space that obeys Kolmogorov's zero-one law. All Bernoulli automorphisms are K-automorphisms (one says they have the K-property), but not vice versa.".
- Kolmogorov_automorphism label "Kolmogorov automorphism".
- Kolmogorov_automorphism sameAs Q6427427.
- Kolmogorov_automorphism sameAs コルモゴロフ自己同型.
- Kolmogorov_automorphism sameAs m.0kfxjzr.
- Kolmogorov_automorphism sameAs Q6427427.
- Kolmogorov_automorphism wasDerivedFrom Kolmogorov_automorphism?oldid=641097468.
- Kolmogorov_automorphism isPrimaryTopicOf Kolmogorov_automorphism.