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如果你知道Varian在成为经济学家之前是研究动态系统的，想有所成就的经济学者应该学习动态系统。如果一个经济学者觉得大数据和机器学习会是很有用的研究工具，也该学习一下“遍历理论”。而这本教材是经典之一。
Ulrich Krengel
Ergodic Theorems
With 21 Supplement by Antoine Brunel
Chapter 1: Measure preserving and null preserving point mappings ....... 1
§ 1.1 Von Neumann’s mean ergodic theorem, ergodicity .............. 1
§ 1.2 Birkhofi”s ergodic theorem .................................. 7
§ 1.3 Recurrence ................................................ 16
§ 1.4 Shift transformations and stationary processes ................. 22
§ 1.5 Kingman’s subadditive ergodic theorem and
the multiplicative ergodic theorem of Oseledec ................. 35
§ 1.6 Relatives of the maximal ergodic theorem ..................... 50
§ 1.7 Some general tools and principles ............................ 63
Chapter 2: Mean ergodic theory .................................... 71
§2.1 The mean ergodic theorem .................................. 71
§ 2.2 Uniform convergence ....................................... 86
§2.3 Weak mixing, continuous spectrum and multiple recurrence ...... 94
§2.4 The splitting theorem of Jacobs-Deleeuw-Glicksberg ............ 103
Chapter 3: Positive contractions in L1 ............................... 113
§3.1 The Hopf decomposition .................................... 113
§3.2 The Chacon-Ornstein theorem ............................... 119
§3.3 Brunel’s lemma and the identification of the limit ............... 123
§3.4 Existence of finite invariant measures ......................... 135
§3.5 The subadditive ergodic theorem for positive contractions in L1 . . 146
§3.6 An example with divergence of Cesaro averages ................ 151
§3.7 More on the filling scheme .................................. 154
Chapter 4.‘ Extensions of the Ll-theory .............................. 159
§4.1 Non positive contractions in L1 ' ............................. 159
§4.2 Vector valued ergodic theorems .............................. 167
§4.3 Power bounded operators and harmonic functions .............. 172
Chapter 5: Operators in C(K) and in LP, (1 <p < oo) .................. 177
§5.1 Markov operators in C (K) .................................. 177
§ 5.2 Contractions in LP, (1 <p < oo) .............................. 186
Chapter 6: Pointwise ergodic theorems for multiparameter and amenable
semigroups ...................................................... 195
§6.1 Unrestricted convergence for averages over d—dimensional
intervals .................................................. 195
§6.2 Multiparameter additive and subadditive processes ............. 201
§6.3 Multiparameter semigroups of Ll-contractions ................. 211
§ 6.4 Amenable semigroups ...................................... 221
Chapter 7: Local ergodic theorems and a’iflerentiation .................. 229
§7.1 Positive 1-parameter semigroups ............................. 229
§7.2 Local ergodic theorems for multiparameter and non positive
semigroups, and for vector valued functions ................... 243
Chapter 8: Subsequences and generalized means ....................... 251
§8.1 Strong convergence and mixing .............................. 251
§ 8.2 Pointwise convergence ...................................... 257
Chapter 9: Special topics .......................................... 267
§9.1 Ergodic theorems in von Neumann algebras ................... 267
§9.2 Entropy and information .................................... 281
§9.3 Nonlinear nonexpansive mappings ............................ 288
§ 9.4 Miscellanea ............................................... 297
Supplement: Harris Processes, Special Functions, Zero-Two-Law
(by Antoine Brunel) .............................................. 301
Bibliography .................................................... 321
Notation ....................................................... 347
Index .......................................................... 3S1
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