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 Caratheodory extension theorem. It also develops the Lebesgue theory of integration, including the dominated convergence theorem and an introduction to the Lebesgue $Lp$spaces.
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Zielgruppe
Für höhere Schule und Studium
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ISBN-13
978-0-8218-4420-5 (9780821844205)
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Schweitzer Klassifikation
Introduction Lebesgue measure Recurrence and ergodicity The Lebesgue integral The ergodic theorem Mixing notions Appendix A. Set notation and the completeness of $\mathbb{R}$ Appendix B. Topology of $\mathbb{R}$ and metric spaces Bibliographical notes Bibliography Index.
