LEADER 05230nam 2200697 a 450 001 9910464534003321 005 20200520144314.0 010 $a1-283-23477-7 010 $a9786613234773 010 $a981-4324-59-0 035 $a(CKB)3400000000016253 035 $a(EBL)840570 035 $a(OCoLC)748215459 035 $a(SSID)ssj0000537511 035 $a(PQKBManifestationID)12251896 035 $a(PQKBTitleCode)TC0000537511 035 $a(PQKBWorkID)10553370 035 $a(PQKB)10682822 035 $a(MiAaPQ)EBC840570 035 $a(WSP)00007933 035 $a(Au-PeEL)EBL840570 035 $a(CaPaEBR)ebr10493518 035 $a(CaONFJC)MIL323477 035 $a(EXLCZ)993400000000016253 100 $a20110608d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHenstock-Kurzweil integration on euclidean spaces$b[electronic resource] /$fLee Tuo Yeong 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$dc2011 215 $a1 online resource (325 p.) 225 1 $aSeries in real analysis ;$vv. 12 300 $aDescription based upon print version of record. 311 $a981-4324-58-2 320 $aIncludes bibliographical references and indexes. 327 $aPreface; Contents; 1. The one-dimensional Henstock-Kurzweil integral; 1.1 Introduction and Cousin's Lemma; 1.2 Definition of the Henstock-Kurzweil integral; 1.3 Simple properties; 1.4 Saks-Henstock Lemma; 1.5 Notes and Remarks; 2. The multiple Henstock-Kurzweil integral; 2.1 Preliminaries; 2.2 The Henstock-Kurzweil integral; 2.3 Simple properties; 2.4 Saks-Henstock Lemma; 2.5 Fubini's Theorem; 2.6 Notes and Remarks; 3. Lebesgue integrable functions; 3.1 Introduction; 3.2 Some convergence theorems for Lebesgue integrals; 3.3 ?m-measurable sets; 3.4 A characterization of ?m-measurable sets 327 $a3.5 ?m-measurable functions3.6 Vitali Covering Theorem; 3.7 Further properties of Lebesgue integrable functions; 3.8 The Lp spaces; 3.9 Lebesgue's criterion for Riemann integrability; 3.10 Some characterizations of Lebesgue integrable functions; 3.11 Some results concerning one-dimensional Lebesgue integral; 3.12 Notes and Remarks; 4. Further properties of Henstock-Kurzweil integrable functions; 4.1 A necessary condition for Henstock-Kurzweil integrability; 4.2 A result of Kurzweil and Jarn ??k; 4.3 Some necessary and su cient conditions for Henstock- Kurzweil integrability 327 $a4.4 Harnack extension for one-dimensional Henstock-Kurzweil integrals4.5 Other results concerning one-dimensional Henstock- Kurzweil integral; 4.6 Notes and Remarks; 5. The Henstock variational measure; 5.1 Lebesgue outer measure; 5.2 Basic properties of the Henstock variational measure; 5.3 Another characterization of Lebesgue integrable functions; 5.4 A result of Kurzweil and Jarn ??k revisited; 5.5 A measure-theoretic characterization of the Henstock- Kurzweil integral; 5.6 Product variational measures; 5.7 Notes and Remarks; 6. Multipliers for the Henstock-Kurzweil integral 327 $a6.1 One-dimensional integration by parts6.2 On functions of bounded variation in the sense of Vitali; 6.3 The m-dimensional Riemann-Stieltjes integral; 6.4 A multiple integration by parts for the Henstock-Kurzweil integral; 6.5 Kurzweil's multiple integration by parts formula for the Henstock-Kurzweil integral; 6.6 Riesz Representation Theorems; 6.7 Characterization of multipliers for the Henstock-Kurzweil integral; 6.8 A Banach-Steinhaus Theorem for the space of Henstock- Kurzweil integrable functions; 6.9 Notes and Remarks; 7. Some selected topics in trigonometric series 327 $a7.1 A generalized Dirichlet test7.2 Fourier series; 7.3 Some examples of Fourier series; 7.4 Some Lebesgue integrability theorems for trigonometric series; 7.5 Boas' results; 7.6 On a result of Hardy and Littlewood concerning Fourier series; 7.7 Notes and Remarks; 8. Some applications of the Henstock-Kurzweil integral to double trigonometric series; 8.1 Regularly convergent double series; 8.2 Double Fourier series; 8.3 Some examples of double Fourier series; 8.4 A Lebesgue integrability theorem for double cosine series; 8.5 A Lebesgue integrability theorem for double sine series 327 $a8.6 A convergence theorem for Henstock-Kurzweil integrals 330 $aThe Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Per 410 0$aSeries in real analysis ;$vv. 12. 606 $aHenstock-Kurzweil integral 606 $aLebesgue integral 606 $aCalculus, Integral 608 $aElectronic books. 615 0$aHenstock-Kurzweil integral. 615 0$aLebesgue integral. 615 0$aCalculus, Integral. 676 $a515.43 700 $aLee$b Tuo Yeong$f1967-$0959523 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910464534003321 996 $aHenstock-Kurzweil integration on euclidean spaces$92174340 997 $aUNINA LEADER 03683oam 2200625 450 001 9910447051803321 005 20230621140743.0 010 $a0-472-90257-1 010 $a0-472-12234-7 024 7 $a10.3998/mpub.9221214 035 $a(CKB)3710000000886526 035 $a(MiAaPQ)EBC4710347 035 $a(OCoLC)959956382 035 $a(MdBmJHUP)muse54288 035 $a(MiU)10.3998/mpub.9221214 035 $a(ScCtBLL)4364f65f-e8f2-478d-91e0-5cdb45b04b58 035 $a(MiAaPQ)EBC6533238 035 $aEBL6533238 035 $a(AU-PeEL)EBL6533238 035 $a(EXLCZ)993710000000886526 100 $a20160623h20162016 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 00$aThree-way street $eJews, Germans, and the transnational /$fJay Howard Geller and Leslie Morris, editors 210 1$aAnn Arbor :$cUniversity of Michigan Press,$d[2016] 215 $a1 online resource (361 pages) $ccolor illustrations 225 1 $aSocial history, popular culture, and politics in Germany 300 $aDescription based upon print version of record. 311 $a0-472-13012-9 320 $aIncludes bibliographical references and index. 330 $a"As German Jews emigrated in the 19th and early 20th centuries and as exiles from Nazi Germany, they carried the traditions, culture, and particular prejudices of their home with them. At the same time, Germany--and Berlin in particular--attracted both secular and religious Jewish scholars from eastern Europe. They engaged in vital intellectual exchange with German Jewry, although their cultural and religious practices differed greatly, and they absorbed many cultural practices that they brought back to Warsaw or took with them to New York and Tel Aviv. After the Holocaust, German Jews and non-German Jews educated in Germany were forced to reevaluate their essential relationship with Germany and Germanness as well as their notions of Jewish life outside of Germany. Among the first volumes to focus on German-Jewish transnationalism, this interdisciplinary collection spans the fields of history, literature, film, theater, architecture, philosophy, and theology as it examines the lives of significant emigrants. The individuals whose stories are reevaluated include German Jews Ernst Lubitsch, David Einhorn, and Gershom Scholem, the architect Fritz Nathan and filmmaker Helmar Lerski; and eastern European Jews David Bergelson, Der Nister, Jacob Katz, Joseph Soloveitchik, and Abraham Joshua Heschel--figures not normally associated with Germany. Three-Way Street addresses the gap in the scholarly literature as it opens up critical ways of approaching Jewish culture not only in Germany, but also in other locations, from the mid-19th century to the present"--$cProvided by publisher. 410 0$aSocial history, popular culture, and politics in Germany 606 $aJews$zGermany$xHistory 606 $aJews, German$zForeign countries 606 $aJews, German, in literature 607 $aGermany$xEmigration and immigration 607 $aGermany$xCivilization$xJewish influences 608 $aBiographies$2lcgft 615 0$aJews$xHistory. 615 0$aJews, German 615 0$aJews, German, in literature. 676 $a305.892/4043 686 $aHIS022000$aHIS054000$aHIS014000$2bisacsh 702 $aMorris$b Leslie$f1958- 702 $aGeller$b Jay Howard 712 02$aMichigan Publishing (University of Michigan) 801 0$bMiU 801 1$bMiU 906 $aBOOK 912 $a9910447051803321 996 $aThree-way street$92029307 997 $aUNINA