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
... limit is defined2 . ) Studying limits of sets together with limits of elements may have been very natural in this ... lower and upper limits of sequences of sets , which are , so to speak , " thick " limits and cluster points respectively : ...
... lower limit of the graphs of the approximate maps Fn , while stability is the boundedness of the inverses of the derivatives of the maps Fn . This provides a first motivation for devising a set - valued dif- ferential calculus . For ...
... limits and cluster points of sequences of elements to sequences of sets . These set - valued analogues have been introduced by Painlevé in 1902 under the names of upper and lower limits of sets . They were then popular- ized by ...
... Limits of sets have been introduced by Painlevé3 in 1902 , as it is reported by his student Zoretti . They have been popularized by Kuratowski in his famous book TOPOLOGIE and thus , often called Kuratowski lower and upper limits of ...
... Lower and upper limits are obviously closed . We also see at once that Liminfn → ∞ Kn C Limsupn → ∞ Kn and that ... limit , which is the intersection of their closures : if Kn C Km when n≥m , then Limn → ∞ Kn = n Kn n > 0 An upper ...