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003 | RU-ToGU | ||
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007 | cr nn 008mamaa | ||
008 | 160915s2014 sz | s |||| 0|eng d | ||
020 |
_a9783034806947 _9978-3-0348-0694-7 |
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024 | 7 |
_a10.1007/978-3-0348-0694-7 _2doi |
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035 | _ato000541803 | ||
040 |
_aSpringer _cSpringer _dRU-ToGU |
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050 | 4 | _aQA331.5 | |
072 | 7 |
_aPBKB _2bicssc |
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072 | 7 |
_aMAT034000 _2bisacsh |
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072 | 7 |
_aMAT037000 _2bisacsh |
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082 | 0 | 4 |
_a515.8 _223 |
100 | 1 |
_aLerner, Nicolas. _eauthor. _9327376 |
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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. |
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300 |
_aXVIII, 492 p. 15 illus., 3 illus. in color. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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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 |
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650 | 1 | 4 |
_aMathematics. _9566184 |
650 | 2 | 4 |
_aReal Functions. _9304716 |
650 | 2 | 4 |
_aMeasure and Integration. _9303749 |
710 | 2 |
_aSpringerLink (Online service) _9143950 |
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773 | 0 | _tSpringer eBooks | |
856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-3-0348-0694-7 |
912 | _aZDB-2-SMA | ||
999 | _c399899 |