Basic Ergodic Theory (Google eBook)

Front Cover
Springer, Jan 1, 1998 - Mathematics - 149 pages
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This is an introductory book on ergodic theory. The presentation has a slow pace and the book can be read by anyone with a background in basic measure theory and metric topology. In particular, the first two chapters, the elements of ergodic theory, can form a course of four to six lectures at the advanced undergraduate or the beginning graduate level. A new feature of the book is that the basic topics of ergodic theory such as the Poincaré recurrence lemma, induced automorphisms and Kakutani towers, compressibility and E. Hopf's theorem, the theorem of Ambrose on representation of flows are treated at the descriptive set-theoretic level before their measure-theoretic or topological versions are presented. In addition, topics centering around the Glimm-Effros theorem are discussed, topics which have so far not found a place in texts on ergodic theory. In this second edition, a section on rank one automorphisms and a brief discussion of the ergodic theorem due to Wiener and Wintner have been added. "This relatively short book is, for anyone new to ergodic theory, admirably broad in scope. The exposition is clear, and the brevity of the book has not been achieved by giving terse proofs. The examples have been chosen with great care. Historical facts and many references serve to help connect the reader with literature that goes beyond the content of the book as well as explaining how the subject developed. It is easy to recommend this book for students as well as anyone who would like to learn about the descriptive approach to ergodic theory." (Summary of a review of the first edition in Math Reviews)
  

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Contents

I
vii
II
ix
III
1
IV
2
V
3
VI
6
VII
7
VIII
10
XXXII
67
XXXIV
68
XXXV
69
XXXVI
71
XXXVII
72
XXXVIII
73
XXXIX
75
XL
79

IX
13
X
15
XI
16
XII
20
XIII
27
XIV
29
XV
31
XVI
33
XVIII
36
XIX
39
XX
43
XXI
51
XXII
54
XXIII
55
XXIV
56
XXV
57
XXVII
58
XXVIII
61
XXIX
63
XXXI
65
XLI
83
XLII
93
XLIII
95
XLIV
96
XLV
99
XLVI
104
XLVII
109
XLVIII
110
XLIX
111
L
113
LI
125
LII
126
LIII
128
LIV
131
LV
134
LVI
138
LVII
141
LVIII
147
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About the author (1998)

Nadkarni, University of Mumbai, India.

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