LEADER 04499nam 22007575 450 001 9910741160603321 005 20200703222931.0 010 $a1-4471-5122-4 024 7 $a10.1007/978-1-4471-5122-7 035 $a(CKB)2670000000393912 035 $a(SSID)ssj0000936071 035 $a(PQKBManifestationID)11530742 035 $a(PQKBTitleCode)TC0000936071 035 $a(PQKBWorkID)10961784 035 $a(PQKB)11075178 035 $a(DE-He213)978-1-4471-5122-7 035 $a(MiAaPQ)EBC6311478 035 $a(MiAaPQ)EBC1317449 035 $a(Au-PeEL)EBL1317449 035 $a(CaPaEBR)ebr10983410 035 $a(OCoLC)870244243 035 $a(PPN)170487075 035 $a(EXLCZ)992670000000393912 100 $a20130614d2013 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aReal Analysis: Measures, Integrals and Applications /$fby Boris Makarov, Anatolii Podkorytov 205 $a1st ed. 2013. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2013. 215 $a1 online resource (XIX, 772 p. 23 illus.) 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4471-5121-6 320 $aIncludes bibliographical references and index. 327 $aMeasure -- The Lebesgue Model -- Measurable Functions -- The Integral -- The Product Measure -- Change of Variables in an Integral -- Integrals Dependent on a Parameter -- Surface Integrals -- Approximation and Convolution of the Space -- Fourier Series and the Fourier Transform -- Charges. The Radon-Nikodym Theory -- Integral Representation of Linear Functionals -- Appendices. 330 $aReal Analysis: Measures, Integrals and Applications is devoted to the basics of integration theory and its related topics. The main emphasis is made on the properties of the Lebesgue integral and various applications both classical and those rarely covered in literature.   This book provides a detailed introduction to Lebesgue measure and integration as well as the classical results concerning integrals of multivariable functions. It examines the concept of the Hausdorff measure, the properties of the area on smooth and Lipschitz surfaces, the divergence formula, and Laplace's method for finding the asymptotic behavior of integrals. The general theory is then applied to harmonic analysis, geometry, and topology. Preliminaries are provided on probability theory, including the study of the Rademacher functions as a sequence of independent random variables.   The book contains more than 600 examples and exercises. The reader who has mastered the first third of the book will be able to study other areas of mathematics that use integration, such as probability theory, statistics, functional analysis, partial probability theory, statistics, functional analysis, partial differential equations and others.   Real Analysis: Measures, Integrals and Applications is intended for advanced undergraduate and graduate students in mathematics and physics. It assumes that the reader is familiar with basic linear algebra and differential calculus of functions of several variables. 410 0$aUniversitext,$x0172-5939 606 $aMeasure theory 606 $aFourier analysis 606 $aFunctions of real variables 606 $aGeometry 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 615 0$aMeasure theory. 615 0$aFourier analysis. 615 0$aFunctions of real variables. 615 0$aGeometry. 615 14$aMeasure and Integration. 615 24$aFourier Analysis. 615 24$aReal Functions. 615 24$aGeometry. 676 $a515 700 $aMakarov$b Boris$4aut$4http://id.loc.gov/vocabulary/relators/aut$0521456 702 $aPodkorytov$b Anatolii$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910741160603321 996 $aReal Analysis: Measures, Integrals and Applications$93554024 997 $aUNINA