TY  - BOOK
AU  - Silva,C.E.
TI  - Invitation to ergodic theory 
T2  - Student mathematical library
SN  - 9780821887332
PY  - 2008///
CY  - Providence
PB  - American Mathematical Society
KW  - Ergodic theory
KW  - Lebesgue measure
KW  - Recurrence and ergodicity
KW  -  Ergodic theorem
KW  - Mixing notions
N1  - Includes bibliographical references and index
N2  - 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 
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
ER  -