LEADER 02673nam 22004695 450 001 9910300103403321 005 20200703061811.0 010 $a981-13-0938-8 024 7 $a10.1007/978-981-13-0938-0 035 $a(CKB)4100000007110977 035 $a(DE-He213)978-981-13-0938-0 035 $a(MiAaPQ)EBC6315326 035 $a(PPN)232469415 035 $a(EXLCZ)994100000007110977 100 $a20181104d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aReal and Complex Analysis $eVolume 1 /$fby Rajnikant Sinha 205 $a1st ed. 2018. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2018. 215 $a1 online resource (IX, 637 p.) 311 $a981-13-0937-X 327 $aChapter 1. Lebesgue Integration -- Chapter 2. Lp-Spaces -- Chapter 3. Fourier Transforms -- Chapter 4. Holomorphic and Harmonic Functions -- Chapter 5. Conformal Mapping -- Chapter 6. Analytic Continuation -- Chapter 7. Special Functions. 330 $aThis is the first volume of the two-volume book on real and complex analysis. This volume is an introduction to measure theory and Lebesgue measure where the Riesz representation theorem is used to construct Lebesgue measure. Intended for undergraduate students of mathematics and engineering, it covers the essential analysis that is needed for the study of functional analysis, developing the concepts rigorously with sufficient detail and with minimum prior knowledge of the fundamentals of advanced calculus required. Divided into three chapters, it discusses exponential and measurable functions, Riesz representation theorem, Borel and Lebesgue measure, -spaces, Riesz?Fischer theorem, Vitali?Caratheodory theorem, the Fubini theorem, and Fourier transforms. Further, it includes extensive exercises and their solutions with each concept. The book examines several useful theorems in the realm of real and complex analysis, most of which are the work of great mathematicians of the 19th and 20th centuries. 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aAnalysis. 676 $a515 700 $aSinha$b Rajnikant$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721177 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300103403321 996 $aReal and complex analysis$91563610 997 $aUNINA