Contents
Preface «
I Basic concepts. 1
1.1 Stationary processes 1
1.2 The ergodic theory model 13
1.3 The ergodic theorem 33
1.4 Frequencies of finite blocks 43
1.5 The entropy theorem 51
1.6 Entropy as expected value ". 56
1.7 Interpretations of entropy. 66
1.8 Stationary coding 79
1.9 Process topologies 87
1.10 Cutting and stacking 103
II Entropy-related properties. 121
II.l Entropy and coding 121
n.2 The Lempel-Ziv algorithm 131
n.3 Empirical entropy. 137
II.4 Partitions of sample paths 147
n.5 Entropy and recurrence times 154
III Entropy for restricted classes. 165
III.1 Rates of convergence 165
III.2 Entropy and joint distributions 174
III.3 The J-admissibility problem 184
III.4 Blowing-up properties 194
III.5 The waiting-time problem 200
IV B-processes. 211
IV.l Almost block-independence 211
IV.2 The finitely determined property 221
IV.3 Other B-process characterizations 232
Bibliography 239
Index 245
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