LEADER 03574nam 22006975 450 001 9910349334503321 005 20200701212939.0 010 $a9783030187477 010 $a3030187470 024 7 $a10.1007/978-3-030-18747-7 035 $a(CKB)4100000009362584 035 $a(DE-He213)978-3-030-18747-7 035 $a(MiAaPQ)EBC5924712 035 $a(PPN)269148590 035 $a(MiAaPQ)EBC31887852 035 $a(Au-PeEL)EBL31887852 035 $a(OCoLC)1121075933 035 $a(EXLCZ)994100000009362584 100 $a20190917d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMeasure and Integration /$fby Satish Shirali, Harkrishan Lal Vasudeva 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XII, 598 p.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 311 08$a9783030187460 311 08$a3030187462 327 $a1 Preliminaries -- 2 Measure in Euclidean Space -- 3 Measure Spaces and Integration -- 4 Fourier Series -- 5 Differentiation -- 6 Lebesgue Spaces and Modes of Convergence -- 7 Product Measure and Completion -- 8 Hints -- References -- Index. 330 $aThis textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis. Proceeding at a leisurely, student-friendly pace, the authors begin by recalling elementary notions of real analysis before proceeding to measure theory and Lebesgue integration. Further chapters cover Fourier series, differentiation, modes of convergence, and product measures. Noteworthy topics discussed in the text include Lp spaces, the Radon?Nikody?m Theorem, signed measures, the Riesz Representation Theorem, and the Tonelli and Fubini Theorems. This textbook, based on extensive teaching experience, is written for senior undergraduate and beginning graduate students in mathematics. With each topic carefully motivated and hints to more than 300 exercises, it is the ideal companion for self-study or use alongside lecture courses. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aMeasure theory 606 $aFunctions of real variables 606 $aFourier analysis 606 $aFunctional analysis 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 615 0$aMeasure theory. 615 0$aFunctions of real variables. 615 0$aFourier analysis. 615 0$aFunctional analysis. 615 14$aMeasure and Integration. 615 24$aReal Functions. 615 24$aFourier Analysis. 615 24$aFunctional Analysis. 676 $a515.43 676 $a515.43 700 $aShirali$b Satish$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767697 702 $aVasudeva$b Harkrishan Lal$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349334503321 996 $aMeasure and Integration$92510591 997 $aUNINA