Mathematical Theory of Entropy
Cambridge University Press, Jun 2, 2011 - Mathematics - 286 pages
Originally published in 1981, this excellent treatment of the mathematical theory of entropy gives an accessible exposition of the ways in which this idea has been applied to information theory, ergodic theory, topological dynamics and statistical mechanics. Scientists who want a quick understanding of how entropy is applied in disciplines not their own, or simply desire a better understanding of the mathematical foundation of the entropy function will find this to be a valuable book.
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a-field alphabet atoms Bernoulli shift Bernoulli systems block encoder called canonical family channel collection compact complete mod Corollary countable countable partition cylinder sets defined definition denote discrete probability distribution disjoint dynamical system Equation equivalent ergodic theory event factor space factor space associated family of measures finite entropy finite measurable partition finite partition finite set finite subset finitely determined follows given gives implies independent partition infinite invertible dynamical system Kakutani Lebesgue measure Lebesgue space martingale mathematical measure preserving measure space memoryless metric automorphism metric space nonnegative Notice obtained open cover ordered partition Ornstein outcome partition of fl point partition positive integer probability measure probability space Proof prove random variable rate of information real number result Rohlin Section sliding block encoder space ft stationary stochastic process stochastic sequence Suppose Tail(T tion topological entropy transformation uncertainty weak Bernoulli zero partition