Ergodic theory / Karl PetersenType de document : MonographieCollection : Cambridge studies in advanced mathematics, 2Langue : anglais.Pays : Grande Bretagne.Éditeur : Cambridge : Cambridge University Press, 1983Description : 1 vol. (XI-329 p.) : fig. ; 24 cmISBN : 9780521389976.ISSN : 0950-6330.Bibliographie : Bibliogr. p. -321. Index.Sujet MSC : 28Dxx, Measure and integration - Measure-theoretic ergodic theory
28-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
37Bxx, Dynamical systems and ergodic theory - Topological dynamicsEn-ligne : MathSciNet
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This book is one of several on ergodic theory which have appeared in the past few years. It is a well-written treatment of basic ergodic theory with further development in several areas which are presently actively researched.
One nice feature of the book is a development of the method of maximal functions and its use in treating the ergodic Hilbert transform, proving the pointwise ergodic theorem, Lebesgue's differentiation theorem, and Wiener's local ergodic theorem. Two other nice features are the introduction of almost periodicity and its application in constructing eigenfunctions for nonweakly mixing ergodic transformations, and the Jewett-Bellow-Furstenberg proof of Krieger's theorem on the representation of ergodic measure-preserving transformations. (MathSciNet)
Bibliogr. p. -321. Index