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008 160915s2014 sz | s |||| 0|eng d
020 _a9783034806947
_9978-3-0348-0694-7
024 7 _a10.1007/978-3-0348-0694-7
_2doi
035 _ato000541803
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA331.5
072 7 _aPBKB
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.8
_223
100 1 _aLerner, Nicolas.
_eauthor.
_9327376
245 1 2 _aA Course on Integration Theory
_helectronic resource
_bincluding more than 150 exercises with detailed answers /
_cby Nicolas Lerner.
260 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2014.
300 _aXVIII, 492 p. 15 illus., 3 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
505 0 _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.
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 Carathéodory 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.
650 0 _amathematics.
_9566183
650 1 4 _aMathematics.
_9566184
650 2 4 _aReal Functions.
_9304716
650 2 4 _aMeasure and Integration.
_9303749
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0694-7
912 _aZDB-2-SMA
999 _c399899