Set-Valued Analysis"An elegantly written, introductory overview of the field, with a near perfect choice of what to include and what not, enlivened in places by historical tidbits and made eminently readable throughout by crisp language. It has succeeded in doing the near-impossible—it has made a subject which is generally inhospitable to nonspecialists because of its ‘family jargon’ appear nonintimidating even to a beginning graduate student." —The Journal of the Indian Institute of Science "The book under review gives a comprehensive treatment of basically everything in mathematics that can be named multivalued/set-valued analysis. It includes...results with many historical comments giving the reader a sound perspective to look at the subject...The book is highly recommended for mathematicians and graduate students who will find here a very comprehensive treatment of set-valued analysis." —Mathematical Reviews "I recommend this book as one to dig into with considerable pleasure when one already knows the subject...‘Set-Valued Analysis’ goes a long way toward providing a much needed basic resource on the subject." —Bulletin of the American Mathematical Society "This book provides a thorough introduction to multivalued or set-valued analysis...Examples in many branches of mathematics, given in the introduction, prevail [upon] the reader the indispensability [of dealing] with sequences of sets and set-valued maps...The style is lively and vigorous, the relevant historical comments and suggestive overviews increase the interest for this work...Graduate students and mathematicians of every persuasion will welcome this unparalleled guide to set-valued analysis." —Zentralblatt Math |
From inside the book
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... bounded families of closed convex processes are bounded — a prerequisite for studying the convergence of closed convex processes. But most important of all, one can transpose closed convex processes and use the benefits of duality ...
... bounded. (We can also replace generalized sequences by "filters.") The upper limit of a generalized sequence of subsets where u ranges over a directed subset M. is the set of cluster points of generalized sequences Xfj, of elements of ...
... bounded subsets of the dual X* are weakly relatively compact. However, in general X is a closed subspace of the bidual X** of X, which is the dual of the Banach space X*, endowed with the norm ||p||* := sup | <p,x > | IWI<i The space X ...
... bounded subset of a finite dimensional vector space X. Then co (Limsup^oo-Kn) = f] co I (J Kn N>0 \n>N Proof — The closed convex hull of the upper limit is obviously contained in the closed convex subset A := fl co I |J Kn N>0 \n>N We ...
... bounded. Then xn remains in a bounded subset, which is weakly relatively compact. Hence it has a cluster point x which belongs to a — Limsup^oo-ftTn. Since A is continuous from X to Y, when they are supplied with their weak topologies ...