In mathematics, the Ornstein isomorphism theorem is a deep result in ergodic theory. It states that if two Bernoulli schemes have the same Kolmogorov entropy...

operator, which may be used to study Bernoulli schemes. The Ornstein isomorphism theorem shows that Bernoulli shifts are isomorphic when their entropy...

limit to the predictability of the system Maximal ergodic theorem Ornstein isomorphism theorem Statistical mechanics Symbolic dynamics Reed, Michael; Simon...

deterministic, and the other being a moving average process. The Ornstein isomorphism theorem states that every stationary stochastic process is equivalent...

distinction to the Bernoulli automorphism. In particular, the Ornstein isomorphism theorem does not apply to K-systems, and so the entropy is not sufficient...

the isomorphism of dynamical systems. The question long defied analysis, but was finally and completely answered with the Ornstein isomorphism theorem. This...

states is known as a Bernoulli process. Note, however, by the Ornstein isomorphism theorem, that every aperiodic and irreducible Markov chain is isomorphic...

Cantor's isomorphism theorem (order theory) Dilworth's theorem (combinatorics, order theory) Four functions theorem (combinatorics) Hahn embedding theorem (ordered...

an open problem. Countable discrete amenable groups obey the Ornstein isomorphism theorem. Finite groups are amenable. Use the counting measure with the...

most celebrated of these is perhaps the Bernoulli flow. The Ornstein isomorphism theorem states that, for any given entropy H, there exists a flow φ(x...

Ya. (1962). "A weak isomorphism of transformations with invariant measure". Doklady Akademii Nauk SSSR. 147: 797–800. Ornstein, D. (1970). "Bernoulli...

is generated by a partition into k {\displaystyle k} subsets. Ornstein isomorphism theorem (Chapter 6 ). Let ( X , T ) {\displaystyle \textstyle (X,T)}...

1007/BF02810577. ISSN 0021-2172. Theorem 6.1 Ornstein, Donald S.; Weiss, Benjamin (1987). "Entropy and isomorphism theorems for actions of amenable groups"...

Bernoulli shifts are classified up to measurable isomorphism by their entropy by Ornstein's theorem, this means that the moduli space of all ergodic compact...

volume integral of the direct correlation function c(r), as defined by the Ornstein-Zernike equation. This length scale grows appreciably with decreasing temperature...