LEADER 03761oam 2200505 450 001 9910484024903321 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 $a9910484024903321 996 $aEssentials of integration theory for analysis$9240450 997 $aUNINA LEADER 00978nam a2200265 i 4500 001 991001207789707536 008 110512s2011 it 000 0 ita d 020 $a9788834320051 035 $ab13977891-39ule_inst 040 $aBiblioteca Interfacoltà$bita 082 04$a292.61 100 1 $aBianchi, Edoardo$0447472 245 13$aIl rex sacrorum a Roma e nell'Italia antica /$cEdoardo Bianchi 260 $aMilano :$bVita e pensiero,$c2011 300 $aIX, 242 p. ;$c24 cm. 440 0$aV&P Università.$pStoria.$pRicerche. 504 $aBibliografia: p. [219]-238 650 4$aSacerdozio$zRoma antica$xStoria 650 4$aReligione romana 907 $a.b13977891$b02-04-14$c12-05-11 912 $a991001207789707536 945 $aLE002 292.61 BIA$g1$i2002000624574$lle002$og$pE0.00$q-$rl$s- $t0$u0$v0$w0$x0$y.i15266515$z12-05-11 996 $aRex sacrorum a Roma e nell'Italia antica$9246650 997 $aUNISALENTO 998 $ale002$b12-05-11$cm$da $e-$fita$git $h3$i0