Ergodic Theory Entropy

Notation, symbols.- Examples.- Ergodic theorem.- Conditional probabilities and expectations. Doob's martingale theorem.- Entropy and conditional entropy.- Entropy of a Transformation.- The Shannon-McMillan-Breiman theorem.- Mixing, kolmogorov-automorphisms.- Isomorphism of bernoulli shifts sinai and Ornstein's theorems.- Entropy and generators. Krieger's theorem.- Discussion.