Basic Ergodic Theory
Nadkarni, M. G
This book treats mainly some basic topics of ergodic theory in a revised form, bringing into focus its interactions with classical descriptive set theory more than is normally the practice. The presentation has a slow pace and can be read by anyone with a background in measure theory and point set topology. In particular, the first two chapters, the core of ergodic theory, can form a course of four to six lectures at third year B. Sc. , M. Sc. , or M. Phil. level in Indian Universities. I have borrowed freely from existing texts ( with acknowledgements) but the overall theme of the book falls in the complement of these. G. W. Mackey has emphasised the need to look at group actions also from a purely descriptive standpoint. This helps clarify ideas and leads to sharper theo rems even for the case of a single transformation. With this in view, basic topics of ergodic theory such as the Poincare recurrence lemma, induced automorphisms and Kakutani towers, compressibility and HopPs theorem, the Ambrose represen tation of flows etc. are treated at the descriptive level before appearing in their measure theoretic or topological versions. In addition, topics centering around the Glimm-Effros theorem are discussed. These topics have so far not found a place in texts on ergodic theory. Dye's theorem, proved at the measure theoretic level in Chapter 11, when combined with some descriptive results of earlier chapters, becomes a very neat theorem of descriptive set theory
种类:
年:
1995
出版:
Softcover reprint of the original 1st ed. 1995
出版社:
Birkhäuser, Birkhäuser Basel, Imprint
语言:
english
页:
150
ISBN 10:
3034897952
ISBN 13:
9783034897952
系列:
Birkhäuser Advanced Texts Basler Lehrbücher
文件:
DJVU, 1.20 MB
IPFS:
,
english, 1995