LEADER 03759oam 2200505 450 001 996418189503316 005 20210618142303.0 010 $a3-030-58478-X 010 $a9783030584788 024 7 $a10.1007/978-3-030-58478-8 035 $a(CKB)4100000011610153 035 $a(DE-He213)978-3-030-58478-8 035 $a(MiAaPQ)EBC6455984 035 $a(PPN)252507495 035 $a(EXLCZ)994100000011610153 100 $a20210618d2020 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEssentials of integration theory for analysis /$fDaniel W. Stroock 205 $aSecond edition. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XVI, 285 p. 1 illus.) 225 1 $aGraduate Texts in Mathematics ;$v262 311 $a3-030-58477-1 320 $aIncludes bibliographical references and index. 327 $aPreface -- Notation -- 1. The Classical Theory.-2. Measures. -3. Lebesgue Integration.-4. Products of Measures.-5. Changes of Variable.-6. Basic Inequalities and Lebesgue Spaces.-7. Hilbert Space and Elements of Fourier Analysis.-8. Radon?Nikodym, Hahn, Daniell Integration, and Carathéodory- Index. 330 $aWhen the first edition of this textbook published in 2011, it constituted a substantial revision of the best-selling Birkhäuser title by the same author, A Concise Introduction to the Theory of Integration. Appropriate as a primary text for a one-semester graduate course in integration theory, this GTM is also useful for independent study. A complete solutions manual is available for instructors who adopt the text for their courses. This second edition has been revised as follows: §2.2.5 and §8.3 have been substantially reworked. New topics have been added. As an application of the material about Hermite functions in §7.3.2, the author has added a brief introduction to Schwartz's theory of tempered distributions in §7.3.4. Section §7.4 is entirely new and contains applications, including the Central Limit Theorem, of Fourier analysis to measures. Related to this are subsections §8.2.5 and §8.2.6, where Lévy's Continuity Theorem and Bochner's characterization of the Fourier transforms of Borel probability on ?N are proven. Subsection 8.1.2 is new and contains a proof of the Hahn Decomposition Theorem. Finally, there are several new exercises, some covering material from the original edition and others based on newly added material. From the reviews of the first edition: ?The presentation is clear and concise, and detailed proofs are given. ? Each section also contains a long and useful list of exercises. ? The book is certainly well suited to the serious student or researcher in another field who wants to learn the topic. ?the book could be used by lecturers who want to illustrate a standard graduate course in measure theory by interesting examples from other areas of analysis.? (Lars Olsen, Mathematical Reviews 2012) ??It will help the reader to sharpen his/her sensitivity to issues of measure theory, and to renew his/her expertise in integration theory.? (Vicen?iu D. R?dulescu, Zentralblatt MATH, Vol. 1228, 2012). 410 0$aGraduate texts in mathematics ;$v262. 606 $aMeasure theory 606 $aIntegration, Functional 615 0$aMeasure theory. 615 0$aIntegration, Functional. 676 $a515.42 700 $aStroock$b Daniel W.$042628 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a996418189503316 996 $aEssentials of integration theory for analysis$9240450 997 $aUNISA