Invitation to Ergodic Theory pdf epub mobi txt 电子书 下载 2025
C. E. Silva: Williams College, Williamstown, MA
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This book is an introduction to basic concepts in ergodic theory such as recurrence, ergodicity, the ergodic theorem, mixing, and weak mixing. It does not assume knowledge of measure theory; all the results needed from measure theory are presented from scratch. In particular, the book includes a detailed construction of the Lebesgue measure on the real line and an introduction to measure spaces up to the Carathéodory extension theorem. It also develops the Lebesgue theory of integration, including the dominated convergence theorem and an introduction to the Lebesgue Lp spaces.
Several examples of a dynamical system are developed in detail to illustrate various dynamical concepts. These include in particular the baker's transformation, irrational rotations, the dyadic odometer, the Hajian–Kakutani transformation, the Gauss transformation, and the Chacón transformation. There is a detailed discussion of cutting and stacking transformations in ergodic theory. The book includes several exercises and some open questions to give the flavor of current research. The book also introduces some notions from topological dynamics, such as minimality, transitivity and symbolic spaces; and develops some metric topology, including the Baire category theorem.
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读过一次,还能复习Measure theory. 遍历论本科生入门书, 可以一看, 反正看起来也快.
评分读过一次,还能复习Measure theory. 遍历论本科生入门书, 可以一看, 反正看起来也快.
评分读过一次,还能复习Measure theory. 遍历论本科生入门书, 可以一看, 反正看起来也快.
评分读过一次,还能复习Measure theory. 遍历论本科生入门书, 可以一看, 反正看起来也快.
评分读过一次,还能复习Measure theory. 遍历论本科生入门书, 可以一看, 反正看起来也快.
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