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Introduction

Becker, Howard and Kechris, Alexander S. (1996) Introduction. In: The Descriptive Set Theory of Polish Group Actions. London Mathematical Society Lecture Note Series. No.232. Cambridge University Press , Cambridge, viii-xii. ISBN 9780521576055. http://resolver.caltech.edu/CaltechAUTHORS:20180817-094122252

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Abstract

A Polish space (group) is a separable, completely metrizable topological space (group). This book is about actions of Polish groups, in connection with – or from the point of view of – the subject of descriptive set theory. Descriptive set theory is the study of definable sets and functions in Polish spaces. The basic classes of definable sets are the classes of Borel, analytic and co–analytic sets, and these certainly constitute the main topic of the book, but at times we also consider other classes of definable sets. The structure of Borel actions of Polish locally compact, i.e., second countable locally compact, topological groups has long been studied in ergodic theory, operator algebras and group representation theory. See, for example, Auslander–Moore [66], Feldman–Hahn–Moore [78], Glimm [61], Kechris [92a], Mackey [57, 62, 89], Moore [82], Ramsay [82, 85], Sinai [89], Varadarajan [63], Vershik–Fedorov [87], Zimmer [84] for a sample of this work. This is closely related to the subject matter of this book. More recently, there has been increasing interest in an extension of the above: studying the structure of Borel actions of arbitrary, not necessarily locally compact, Polish groups.


Item Type:Book Section
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Additional Information:© 1996 Cambridge University Press.
Record Number:CaltechAUTHORS:20180817-094122252
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180817-094122252
Official Citation:Becker, H., & Kechris, A. (1996). INTRODUCTION. In The Descriptive Set Theory of Polish Group Actions (London Mathematical Society Lecture Note Series, pp. Viii-Xii). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511735264.002
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88893
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Aug 2018 16:54
Last Modified:17 Aug 2018 16:54

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