## 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 81

Indeed, the two basic theorems on continuous linear operators due to

**Banach**, the Closed Graph Theorem (equivalent to ... The first one states that a closed convex process defined on the whole

**space**is continuous, and the second states ...

The ball of radius r > 0 around K in X is denoted by Bx{K,r) := {xeX \ d(x,K)<r} When there is no ambiguity, we set B(K,r) := Bx(K,r) When X is a

**Banach space**whose unit ball is denoted by B (or Bx if the space must be mentioned) ...

We may need the above extension when dealing with weak topologies of a

**Banach space**X and of its dual denoted by X*. We say that the bilinear map < •, • > (p,x) e X* x X h->< p,x > := p(x) is the duality pairing.

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 is called reflexive if X = X**. In this case, it enjoys both ...

Theorem 1.1.8 Let (Kn)ne-^ be a sequence of closed convex cones of a

**Banach space**X. Then Liminfn^ooKn = (a - Limsupn^0C)ii'r;)_ Proof — Inclusion Liminfn^ooiirn C (a - Limsupn^0O.fi:j7)_ is obvious: If x G Liminfn_>00.

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