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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The subset K being compact, it can be covered by p balls B(yi,eVi). This implies that for all n > No 1.1. Limits of Sets 21 40441_21.pdf.
This implies that for all n > No := max^i,...^ iVVi and V := UB(^'%) i=l the intersections Ln n V are empty. On the other hand, W:=WUV being a neighborhood ...
K'~ is the weak-* limit of a subsequence pni G K~, , inequalities < pn> , xn> > < 0 imply that < p, x >< 0. Conversely, assume that some x G ...
Assumption (1.1) implies that the set Im(A*) + (J f| K N>0n>N contains a ball around zero of radius 7 > 0. Then any p € X*, < 7 can be written, ...
Remark — Actually, Proposition 1.2.5 is equivalent to Proposition 1.2.6: The former used with 1 x A and Ln x Mn implies obviously the latter.