## 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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In the same way that topological concepts are based on the notions of limits and cluster points of

**sequences of elements**, their set-valued analogues are rooted in the concepts of lower and upper limits of sequences of sets, which are, ...

We begin the first section by extending concepts of limits and cluster points of

**sequences of elements**to sequences of sets. These set- valued analogues have been introduced by Painleve in 1902 under the names of upper and lower limits ...

Any decreasing sequence of subsets Kn has a limit, which is the intersection of their closures: if Kn C Km when n > m ... Concerning sequences of singleta {xn}, the set limit, when it exists, is either empty (the

**sequence of elements**xn ...

The upper limit is also equal to the subset of cluster points of "approximate"

**sequences**satisfying: Ve>0, ... A generalized

**sequence**is a map u e M i-> € X An

**element**x € X is the limit of if, for every neighborhood V of x, ...

when N := {a>i, . . . , xn} ranges over the finite subsets of X. In other words, a generalized

**sequence of elements**xp € X converges weakly to x G X if and only if for any q e X*, < q, > converges to < q, x > and a sequence pM € X* ...

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