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In recent years there has been a growing interest in the interactions between descriptive set theory and various aspects of the theory of dynamical systems, including ergodic theory and topological dynamics. This volume contains a collection of survey papers by leading researchers covering a wide variety of recent developments in these subjects and their interconnections. This book provides researchers and graduate students interested in either of these areas with a guide to work done in the other, as well as with an introduction to problems and research directions arising from their interconnections.