Product measure p^ℤ on {0,1}^ℤ together with the left shift σ. Mixing, Kolmogorov, and of Kolmogorov-Sinai entropy H(p). By Ornstein's theorem, two Bernoulli shifts are measurably conjugate iff they have equal entropy.
Product measure p^ℤ on {0,1}^ℤ together with the left shift σ. Mixing, Kolmogorov, and of Kolmogorov-Sinai entropy H(p). By Ornstein's theorem, two Bernoulli shifts are measurably conjugate iff they have equal entropy.