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 35
... Limsup∞Kn CK . Conversely , if X is compact , then the upper limit Limsupn → ∞ Kn enjoys the above property ( and thus , is the smallest closed subset satisfying it . ) Proof- The first statement is obvious . The second one is a ...
... ( Limsup∞ Ln ) whose complement in M is compact . We also provide a useful technical lemma : ᄆ Lemma 1.1.6 Let us consider a sequence of subsets Ln CZ of a metric space Z and a sequence of subsets Mn CY of a compact metric space Y. Let ...
... ( Limsup ; → ∞ K ( m − 1 ) ) + 0 in which case we set K ( m ) nj such that nj K ( m ) : = K ( m - 1 ) , or there exists a subsequence Um ( Limsup ; → ∞ K ( m - 1 ) ) = 0 in which case we set Km ) quence does not. 1.1 . Limits of Sets ...
... ( Limsup ; -∞K ( m ) ) = Um ( Limsup ; ∞ Km - 1 ) ) Ø Pj Since Dn : = K ( n ) = K ( m ) for some pn , we deduce that the sequence ( Dn ) n > m is a subsequence of the sequence ( Km ) ) ; Thus xo € Limsupn∞ Dn C Limsup ; Km ) c X \ Um ...
... Limsup∞ Kn ) Proof- Inclusion Liminfn - Kn C ( o - Limsup∞ Kn ) is obvious : If x Є Liminfn - Kn is the limit of a sequence of elements Xn Є Kn and pЄo - Limsupn → ∞ Kn is the weak - ✩ limit of a subsequence pn ' € K , inequalities ...