## Entropy and generators in ergodic theory |

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a-algebra a-finite a-generator with finite Affine transformations Akad ALGEBRAIC Anosov diffeomorphism arbitrary Bernoulli canonical measures Chapter choose conditional entropy Consequently convergence theorems Corollary 4.30 countable measurable partition countable partition d(Tnx distal Dokl dynamical systems element endomorphism equivalence ergodic automorphism ergodic theory exists a countable finite deficiency finite entropy finite partition follows G(mod h(TA H(tj H(Tn Halmos Individual Ergodic Theorem inequality integral invariant measure ir(T isomorphism Jacobian Jean-Pierre Serre K-automorphisms Lebesgue measure Lebesgue space Lemma log m1 Math measure space measure-preserving transformation metric abelian group metric space minimal mn(B morphism n=l n Nauk non-negative one-one Parry PRINCIPAL PARTITIONS Proof quasi-discrete spectrum Remark respect Rohlin Rohlin's theorem Russian sequence Sinai SSSR sub-a-algebra Suppose taking limits Theorem 4.6 tr(T tt(T zero entropy