LEADER 04182nam 22006015 450 001 9910480137703321 005 20200706041454.0 010 $a1-4612-0897-1 024 7 $a10.1007/978-1-4612-0897-6 035 $a(CKB)3400000000089311 035 $a(SSID)ssj0001298255 035 $a(PQKBManifestationID)11690616 035 $a(PQKBTitleCode)TC0001298255 035 $a(PQKBWorkID)11242088 035 $a(PQKB)10568221 035 $a(DE-He213)978-1-4612-0897-6 035 $a(MiAaPQ)EBC3073852 035 $a(PPN)238032884 035 $a(EXLCZ)993400000000089311 100 $a20121227d1993 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aReal and Functional Analysis$b[electronic resource] /$fby Serge Lang 205 $a3rd ed. 1993. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1993. 215 $a1 online resource (XIV, 580 p.) 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v142 300 $aRev. ed. of: Real analysis. 2nd ed. 1983. 311 $a0-387-94001-4 311 $a1-4612-6938-5 320 $aIncludes bibliographical references and index. 327 $aI Sets -- II Topological Spaces -- III Continuous Functions on Compact Sets -- IV Banach Spaces -- V Hilbert Space -- VI The General Integral -- VII Duality and Representation Theorems -- VIII Some Applications of Integration -- IX Integration and Measures on Locally Compact Spaces -- X Riemann-Stieltjes Integral and Measure -- XI Distributions -- XII Integration on Locally Compact Groups -- XIII Differential Calculus -- XIV Inverse Mappings and Differential Equations -- XV The Open Mapping Theorem, Factor Spaces, and Duality -- XVI The Spectrum -- XVII Compact and Fredholm Operators -- XVIII Spectral Theorem for Bounded Hermltian Operators -- XIX Further Spectral Theorems -- XX Spectral Measures -- XXI Local Integration off Differential Forms -- XXII Manifolds -- XXIII Integration and Measures on Manifolds -- Table of Notation. 330 $aThis book is meant as a text for a first year graduate course in analysis. Any standard course in undergraduate analysis will constitute sufficient preparation for its understanding, for instance, my Undergraduate Anal­ ysis. I assume that the reader is acquainted with notions of uniform con­ vergence and the like. In this third edition, I have reorganized the book by covering inte­ gration before functional analysis. Such a rearrangement fits the way courses are taught in all the places I know of. I have added a number of examples and exercises, as well as some material about integration on the real line (e.g. on Dirac sequence approximation and on Fourier analysis), and some material on functional analysis (e.g. the theory of the Gelfand transform in Chapter XVI). These upgrade previous exercises to sections in the text. In a sense, the subject matter covers the same topics as elementary calculus, viz. linear algebra, differentiation and integration. This time, however, these subjects are treated in a manner suitable for the training of professionals, i.e. people who will use the tools in further investiga­ tions, be it in mathematics, or physics, or what have you. In the first part, we begin with point set topology, essential for all analysis, and we cover the most important results. 410 0$aGraduate Texts in Mathematics,$x0072-5285 ;$v142 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aFunctions of real variables 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aFunctions of real variables. 615 14$aAnalysis. 615 24$aReal Functions. 676 $a515 700 $aLang$b Serge$4aut$4http://id.loc.gov/vocabulary/relators/aut$01160 906 $aBOOK 912 $a9910480137703321 996 $aReal and functional analysis$979443 997 $aUNINA