LEADER 01033nam2-2200349li-450- 001 990003231850203316 005 20090429163107.0 035 $a000323185 035 $aUSA01000323185 035 $a(ALEPH)000323185USA01 035 $a000323185 100 $a20090429d1982----km-y0itay50------ba20001109d1994----km-y0itay0103----ba 101 0 $aeng 102 $aUS 105 $a||||||||001yy 200 1 $a<> Problems in analysis$ewith 9 illustrations$fBernard Gelbaum 210 $aNew York [etc.]$cSpringer$dcopyr. 1982 215 $aVII, 228 p.$d23 cm 410 0$12001 454 1$12001 461 1$10010023912$12001$aUnsolved problems in intuitive mathematics 606 0 $aAnalisi funzionale 676 $a515 700 1$aGELBAUM,$bBernard$013074 801 0$aITA$bsalbc$gISBD 912 $a990003231850203316 951 $a510 UPI/3$b9757/CBS$c510$d00218497 959 $aBK 969 $aSCI 979 $aRSIAV7$b90$c20090429$lUSA01$h1631 996 $aProblems in Analysis$9343340 997 $aUNISA LEADER 03889nam 22005895 450 001 9910300141103321 005 20200630181040.0 010 $a3-0348-0694-9 024 7 $a10.1007/978-3-0348-0694-7 035 $a(CKB)3710000000089100 035 $a(Springer)9783034806947 035 $a(MH)013950640-3 035 $a(SSID)ssj0001187094 035 $a(PQKBManifestationID)11773431 035 $a(PQKBTitleCode)TC0001187094 035 $a(PQKBWorkID)11242820 035 $a(PQKB)10412196 035 $a(DE-He213)978-3-0348-0694-7 035 $a(MiAaPQ)EBC3095803 035 $a(PPN)176748237 035 $a(EXLCZ)993710000000089100 100 $a20140225d2014 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Course on Integration Theory $eincluding more than 150 exercises with detailed answers /$fby Nicolas Lerner 205 $a1st ed. 2014. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (XVIII, 492 p. 15 illus., 3 illus. in color.)$conline resource 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-0348-0693-0 320 $aIncludes bibliographical references and index. 327 $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. 330 $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. 606 $aFunctions of real variables 606 $aMeasure theory 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 615 0$aFunctions of real variables. 615 0$aMeasure theory. 615 14$aReal Functions. 615 24$aMeasure and Integration. 676 $a515.8 676 $a515.42 700 $aLerner$b Nicolas$4aut$4http://id.loc.gov/vocabulary/relators/aut$061544 906 $aBOOK 912 $a9910300141103321 996 $aA Course on Integration Theory$92512352 997 $aUNINA 999 $aThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress