## 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

Results 1-5 of 33

In the same way that topological concepts are based on the notions of limits and cluster points of sequences of ... "thick" limits and cluster points respectively: The lower limit of a sequence of

**subsets Kn**is the set of limits of ...

Definition 1.1.1 Let (-

**Kn**)neN be a sequence of

**subsets**of a metric space X. We say that the

**subset**Limsupn_>00. ... the upper limit of the sequence

**Kn**and that the

**subset**Liminfn^ooKn := {x € X \ limn^ood(£,

**Kn**) = 0} is its lower limit.

We also see at once that Liminfn— >oo-Kn C Limsupn—xx, and that the upper limits and lower limits of the

**subsets Kn**and of their closures Kn do coincide, since d(x, Kn) = d(x,Kn). Any decreasing sequence of

**subsets Kn**has a limit, ...

...

**subset**of cluster points of "approximate" sequences satisfying: Ve>0, 3N(e) such that V n > N(e), xn € B(

**Kn**,e) ... we can extend the concepts of upper and lower limits to generalized sequences of

**subsets**of a topological space X. We ...

Instead, for the sake of simplicity, we shall use the concept of sequentially weak upper limit: Definition 1.1.3 Let us consider a sequence of

**subsets Kn**of the dual of a Banach space. We shall say that the subset a - Limsup^ooifn of ...

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