One result in this branch of mathematics is Ornstein's theorema, which gives the conditions under which any two Bernoulli schemes are measure- theoretically isomorphic.
One result in this branch of mathematics is Ornstein's theorema, which gives the conditions under which any two Bernoulli schemes are measure- theoretically isomorphic. Dye's theorem states the existence of isomorphisms between two probability spaces for measure-preserving transformations, and Kolmogorov introduced entropy into it when he applied Shannon's concept of entropy to dynamical systems. Originating 3  in the study of transformations under which the only invariable sets have measure 0 or 1, FTP, identify this branch of mathematics that grew out of a hypothesis that the time average and the average over the statistical ensemble are equivalent.
One result in this branch of mathematics is Ornstein's theorema, which gives the conditions under which any two Bernoulli schemes are measure- theoretically isomorphic.
ergodic theory