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
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... Hence, set- valued analysis inherited the undeserved image of being something difficult and mysterious and, consequently, was regarded as a mathematical curiosity, to be left in the hands of mathematicians who like to generalize for the ...
... Hence the map F which associates with each state x the subset F(x) of feasible velocities is denned by: F(x) := f(x,U(x)) = {f{x,u)}utEU{x) So, the control system governed by the family of parametrized 2 Introduction 40441_2.pdf.
... Hence, we cannot escape the burden of studying measurable maps, which are the maps whose graphs are measurable, and checking in particular that all the standard operations preserve measurability. We also need measurability for defining ...
... Hence we have an easy way to verify upper semicontinuity of a map. Lower semicontinuity is not as simple to check: the last section is devoted to several useful lower semicontinuity criteria. The definitions introduced in this chapter ...
... Hence we have proved that for any e > 0, there exists N > 0 such that V n > N, sup inf tp(z, y) < sup inf ip(z, ?/) + £□ 1.1.2 The Compactness Theorem The Bolzano- Weierstrass Compactness Theorem was adapted in 1927 to the set-valued ...