03574nam 22006975 450 991034933450332120200701212939.09783030187477303018747010.1007/978-3-030-18747-7(CKB)4100000009362584(DE-He213)978-3-030-18747-7(MiAaPQ)EBC5924712(PPN)269148590(MiAaPQ)EBC31887852(Au-PeEL)EBL31887852(OCoLC)1121075933(EXLCZ)99410000000936258420190917d2019 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierMeasure and Integration /by Satish Shirali, Harkrishan Lal Vasudeva1st ed. 2019.Cham :Springer International Publishing :Imprint: Springer,2019.1 online resource (XII, 598 p.) Springer Undergraduate Mathematics Series,1615-20859783030187460 3030187462 1 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.This 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–Nikodým 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.Springer Undergraduate Mathematics Series,1615-2085Measure theoryFunctions of real variablesFourier analysisFunctional analysisMeasure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Real Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12171Fourier Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12058Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Measure theory.Functions of real variables.Fourier analysis.Functional analysis.Measure and Integration.Real Functions.Fourier Analysis.Functional Analysis.515.43515.43Shirali Satishauthttp://id.loc.gov/vocabulary/relators/aut767697Vasudeva Harkrishan Lalauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910349334503321Measure and Integration2510591UNINA