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000697865 020__ $$a9783034806947 $$qelectronic book
000697865 020__ $$a3034806949 $$qelectronic book
000697865 020__ $$z9783034806930
000697865 020__ $$z3034806930
000697865 0247_ $$a10.1007/978-3-0348-0694-7$$2doi
000697865 035__ $$aSP(OCoLC)ocn875182621
000697865 035__ $$aSP(OCoLC)875182621
000697865 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dCOO
000697865 049__ $$aISEA
000697865 050_4 $$aQA312
000697865 08204 $$a515.42$$223
000697865 1001_ $$aLerner, Nicolas,$$d1953-$$eauthor.
000697865 24512 $$aA course on integration theory$$h[electronic resource] :$$bincluding more than 150 exercises with detailed answers /$$cby Nicolas Lerner.
000697865 264_1 $$aBasel :$$bBirkhäuser,$$c2014.
000697865 300__ $$a1 online resource.
000697865 336__ $$atext$$btxt$$2rdacontent
000697865 337__ $$acomputer$$bc$$2rdamedia
000697865 338__ $$aonline resource$$bcr$$2rdacarrier
000697865 504__ $$aIncludes bibliographical references.
000697865 5050_ $$a1 Introduction -- 2 General theory of integration -- 3 Construction of the Lebesgue measure on R^d -- 4 Spaces of integrable functions -- 5 Integration on a product space -- 6 Diffeomorphisms of open subsets of R^d and integration -- 7 Convolution -- 8 Complex measures -- 9 Harmonic analysis -- 10 Classical inequalities.
000697865 506__ $$aAccess limited to authorized users.
000697865 520__ $$aThis textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change-of-variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality, are proven. Further topics include the Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems including Marcinkiewicz's theorem, and the definition of Lebesgue points and the Lebesgue differentiation theorem. Each chapter ends with a large number of exercises and detailed solutions. A comprehensive appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. It also provides more advanced material such as some basic properties of cardinals and ordinals which are useful for the study of measurability.
000697865 588__ $$aDescription based on print version record.
000697865 650_0 $$aMeasure theory.
000697865 650_0 $$aIntegrals, Generalized.
000697865 650_0 $$aMeasure theory$$vProblems, exercises, etc.
000697865 650_0 $$aIntegrals, Generalized$$vProblems, exercises, etc.
000697865 77608 $$iPrint version:$$aLerner, Nicolas, 1953- author.$$tCourse on integration theory$$z9783034806930$$w(OCoLC)870426735
000697865 852__ $$bebk
000697865 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0694-7$$zOnline Access
000697865 909CO $$ooai:library.usi.edu:697865$$pGLOBAL_SET
000697865 980__ $$aEBOOK
000697865 980__ $$aBIB
000697865 982__ $$aEbook
000697865 983__ $$aOnline
000697865 994__ $$a92$$bISE