Handbook of Multivalued Analysis: Volume I: Theory

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This is the first of a two-volume exposition on the theory and applications of set-valued maps. Multivalued analysis is a mixture of many different fields of mathematics, such as topology, measure theory, nonlinear functional analysis and applied mathematics. These two volumes provide a comprehensive survey of the general theory and applications of set-valued analysis. The existing books on the subject deal with either one particular domain of the subject or present primarily the finite dimensional aspects of the theory. In contrast, this volume aims to give a complete picture of the subject, including recent developments. Although the presentation of the subject assumes some knowledge from various areas of mathematical analysis, the authors have made every effort, including the addition of an appendix, to keep the work self-contained. This book serves as a reference for graduate students and researchers interested in multivalued analysis.