Preface

Abstract

This book grew out of a set of notes prepared during the course of a joint Caltech-UCLA Seminar in Descriptive Set Theory and Harmonic Analysis, organized by the authors during the academic year 1985–86. We appreciate very much the help as well as the patience of the participants in this seminar. We are grateful to G. Debs, R. Dougherty, S. Jackson, R. Kaufman, R. Lyons, and J. Saint Raymond for many valuable comments and suggestions. The first author is indebted to S. Pichorides for introducing him to the subject of uniqueness for trigonometric series. We would like also to thank N. O'Connor for her efficiency, care and patience in typing the manuscript. The work of A. S. Kechris has been partially supported by NSF Gratnt DMS84-16349. A. Louveau has been supported by CNRS, France and by UCLA during his visit in the academic year 1985–86. He takes this opportunity to thank the Mathematics Department for its hospitality.

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