An important result in ergodic theory. It states that any two "Bernoulli schemes" with the same measure-theoretic entropy are measure-theoretically isomorphic.
Ornstein's Theorem
See also
Ergodic Theory, Isomorphism, Measure TheoryExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Ornstein's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OrnsteinsTheorem.html