Springer Science & Business Media, Mar 2, 2009 - Science - 461 pages
"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."
"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."
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These set- valued analogues have been introduced by Painleve in 1902 under
the names of upper and lower limits of sets. ... We shall call them simply lower
and upper limits: The lower limit of a sequence of subsets Kn is the set of limits of
Figure 1.1: Example of Upper and Lower Limits of Sets Lower and upper limits
are obviously closed. ... Any decreasing sequence of subsets Kn has a limit,
which is the intersection of their closures: if Kn C Km when n > m, then Limn->oo^
i.e., of limits of subsequences xn> € Kni. The upper limit is also equal to the
subset of cluster points of "approximate" sequences satisfying: Ve>0, 3N(e) such
that V n > N(e), xn € B(Kn,e) Remark — Replacing the balls of a metric space by ...
1.1.4 Convex Hull of Limits Since the distance function to a subset of a normed
space is convex if and only if this subset is convex, we infer that the lower limit of
a ... It is useful to have a characterization of the closed convex hull of upper limit.
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