LEADER 06936nam 2201513 a 450 001 9910789737103321 005 20200520144314.0 010 $a1-283-37995-3 010 $a9786613379955 010 $a1-4008-4269-7 024 7 $a10.1515/9781400842698 035 $a(CKB)2670000000133884 035 $a(EBL)827806 035 $a(OCoLC)769343169 035 $a(SSID)ssj0000575876 035 $a(PQKBManifestationID)11396459 035 $a(PQKBTitleCode)TC0000575876 035 $a(PQKBWorkID)10553953 035 $a(PQKB)11008932 035 $a(StDuBDS)EDZ0001756336 035 $a(DE-B1597)447361 035 $a(OCoLC)979582934 035 $a(DE-B1597)9781400842698 035 $a(Au-PeEL)EBL827806 035 $a(CaPaEBR)ebr10521870 035 $a(CaONFJC)MIL337995 035 $z(PPN)199244979 035 $a(MiAaPQ)EBC827806 035 $a(PPN)187959625 035 $a(EXLCZ)992670000000133884 100 $a20111017d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFre?chet differentiability of Lipschitz functions and porous sets in Banach spaces$b[electronic resource] /$fJoram Lindenstrauss, David Preiss, Jaroslav Tiser 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$d2012 215 $a1 online resource (436 p.) 225 1 $aAnnals of mathematics studies ;$vno. 179 300 $aDescription based upon print version of record. 311 $a0-691-15355-8 311 $a0-691-15356-6 320 $aIncludes bibliographical references and indexes. 327 $t Frontmatter -- $tContents -- $tChapter One: Introduction -- $tChapter Two: Gâteaux differentiability of Lipschitz functions -- $tChapter Three: Smoothness, convexity, porosity, and separable determination -- $tChapter Four: ?-Fréchet differentiability -- $tChapter Five: ?-null and ?n-null sets -- $tChapter Six: Férchet differentiability except for ?-null sets -- $tChapter Seven: Variational principles -- $tChapter Eight: Smoothness and asymptotic smoothness -- $tChapter Nine: Preliminaries to main results -- $tChapter Ten: Porosity, ?n- and ?-null sets -- $tChapter Eleven: Porosity and ?-Fréchet differentiability -- $tChapter Twelve: Fréchet differentiability of real-valued functions -- $tChapter Thirteen: Fréchet differentiability of vector-valued functions -- $tChapter Fourteen: Unavoidable porous sets and nondifferentiable maps -- $tChapter Fifteen: Asymptotic Fréchet differentiability -- $tChapter Sixteen: Differentiability of Lipschitz maps on Hilbert spaces -- $tBibliography -- $tIndex -- $tIndex of Notation 330 $aThis book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics. 410 0$aAnnals of mathematics studies ;$vno. 179. 606 $aBanach spaces 606 $aCalculus of variations 606 $aFunctional analysis 610 $aAsplund space. 610 $aBanach space. 610 $aBorel sets. 610 $aEuclidean space. 610 $aFrechet differentiability. 610 $aFréchet derivative. 610 $aFréchet differentiability. 610 $aFréchet smooth norm. 610 $aGâteaux derivative. 610 $aGâteaux differentiability. 610 $aHilbert space. 610 $aLipschitz function. 610 $aLipschitz map. 610 $aRadon-Nikodým property. 610 $aasymptotic uniform smoothness. 610 $aasymptotically smooth norm. 610 $aasymptotically smooth space. 610 $abump. 610 $acompleteness. 610 $acone-monotone function. 610 $aconvex function. 610 $adeformation. 610 $aderivative. 610 $adescriptive set theory. 610 $aflat surface. 610 $ahigher dimensional space. 610 $ainfinite dimensional space. 610 $airregular behavior. 610 $airregularity point. 610 $alinear operators. 610 $alow Borel classes. 610 $alower semicontinuity. 610 $amean value estimate. 610 $amodulus. 610 $amultidimensional mean value. 610 $anonlinear functional analysis. 610 $anonseparable space. 610 $anull sets. 610 $aperturbation function. 610 $aperturbation game. 610 $aperturbation. 610 $aporosity. 610 $aporous sets. 610 $aregular behavior. 610 $aregular differentiability. 610 $aregularity parameter. 610 $arenorming. 610 $aseparable determination. 610 $aseparable dual. 610 $aseparable space. 610 $aslice. 610 $asmooth bump. 610 $asubspace. 610 $atensor products. 610 $athree-dimensional space. 610 $atwo-dimensional space. 610 $atwo-player game. 610 $avariational principle. 610 $avariational principles. 610 $a?-null sets. 610 $a?-Fréchet derivative. 610 $a?-Fréchet differentiability. 610 $a?-porous sets. 615 0$aBanach spaces. 615 0$aCalculus of variations. 615 0$aFunctional analysis. 676 $a515/.88 686 $aSI 830$2rvk 700 $aLindenstrauss$b Joram$f1936-$041187 701 $aPreiss$b David$0515729 701 $aTis?er$b Jaroslav$f1957-$0515783 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910789737103321 996 $aFréchet differentiability of Lipschitz functions and porous sets in Banach spaces$9854568 997 $aUNINA LEADER 03838nam 22005894a 450 001 9910780388703321 005 20230607214049.0 010 $a1-280-46869-6 010 $a9786610468690 010 $a0-313-01102-8 035 $a(CKB)111087027039326 035 $a(EBL)3000770 035 $a(OCoLC)52718648 035 $a(SSID)ssj0000170989 035 $a(PQKBManifestationID)11176895 035 $a(PQKBTitleCode)TC0000170989 035 $a(PQKBWorkID)10236026 035 $a(PQKB)11783855 035 $a(Au-PeEL)EBL3000770 035 $a(CaPaEBR)ebr10023076 035 $a(MiAaPQ)EBC3000770 035 $a(EXLCZ)99111087027039326 100 $a20011011d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aHigher education in the developing world$b[electronic resource] $echanging contexts and institutional responses /$fedited by David W. Chapman and Ann E. Austin 210 $aWestport, Conn. $cGreenwood Press$d2002 215 $a1 online resource (271 p.) 225 1 $aGreenwood studies in higher education,$x1531-8087 300 $aDescription based upon print version of record. 311 $a0-313-32016-0 320 $aIncludes bibliographical references and index. 327 $aContents; Figures and Tables; Series Foreword; Part I Introduction and Overview; Chapter 1 The Changing Context of Higher Education in the Developing World David W. Chapman and Ann E. Austin; Chapter 2 Higher Education at a Turning Point Jamil Salmi; Part II Seeking a New Balance in Government- University Relationships; Chapter 3 Universities in Transition: Privatization, Decentralization, and Institutional Autonomy as National Policy with Special Reference to the Russian Federation D. Bruce Johnstone and Olga Bain 327 $aChapter 4 Flight from Freedom: Resistance to Institutional Autonomy in Brazil's Federal Universities David N. Plank and Robert E. VerhineChapter 5 When Goals Collide: Higher Education in Laos David W. Chapman; Part III Coping with the Challenges of Greater Autonomy; Chapter 6 Current Challenges and Future Possibilities for the Revitilization of Higher Education in Africa Jairam Reddy; Chapter 7 Higher Education and the State in Mongolia: Dilemmas of Democratic Transition John C. Weidman and Regsurengiin Bat- Erdene 327 $aChapter 8 Chinese Higher Education for the Twenty- First Century: Expansion, Consolidation, and Globalization Gerard A. PostiglionePart IV Achieving Equity While Managing Expansion; Chapter 9 Equity Effects of Higher Education in Developing Countries: Access, Choice, and Persistence Darrell R. Lewis and Halil Dundar; Part V New Pressures and Forms of Accountability; Chapter 10 Quality Assurance for Higher Education: Shaping Effective Policy in Developing Countries Elaine El- Khawas; Part VI Supporting Academic Staff in New Roles 327 $aChapter 11 Context for Higher Education Reform in China: An Analysis of Faculty Issues Yvonna S. Lincoln, Bryan R. Cole, Wang Xiaoping, and Yang "Sherry" XiaoboChapter 12 Academic Staff in Times of Transformation: Roles, Challenges, and Professional Development Needs Ann E. Austin; Part VII Conclusion, Lessons, and Directions; Chapter 13 Balancing Pressures, Forming Partnerships Ann E. Austin and David W. Chapman; Index; About the Contributors 410 0$aGreenwood studies in higher education. 606 $aEducation, Higher$zDeveloping countries 615 0$aEducation, Higher 676 $a378/.009172/4 701 $aChapman$b David W.$f1947-$0867883 701 $aAustin$b Ann E$01536473 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910780388703321 996 $aHigher education in the developing world$93865995 997 $aUNINA