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 38
... For instance, closed maps, that is maps with closed graph, shall play a starring role in this book. It is a weaker property than continuity or even, upper semicontinuity, very familiar and thus easy 6 Introduction 40441_6.pdf.
... weak derivatives of functions and distributions. But each of these extensions was devised for specific purposes (solving partial differential equations, for instance.) When we deal with real-valued functions, we are led to Properties of ...
... 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. We recall that the weakened topology cr(X, X*) of X is defined by the ...
... weak compactness of the unit ball. □ We could for instance use the fact that the weakly compact subsets of the dual X* of a separable5 Banach space are metrizable (for the weak-* topology) (see [148, Theorem 5.6.3]) to avoid ...
... weak upper limit of the polar cones K~ . 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 ...