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Integrationstheorie: Eine Einführung in Die Integrationstheorie Und Ihre Anwendungen

Integrationstheorie: Eine Einführung in Die Integrationstheorie Und Ihre Anwendungen

          
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About the Book

Der vorliegende Text tiber Integration ist aus einem dreisemestrigen Grundkurs "Analysis" hervorgegangen. Diesem Ursprung, wie auch der Erfahrung, daB es den Studenten hoherer Vorlesungen aus der Analysis oder Stochastik haufig an maBtheoretischem Grundwissen mangelt, ent- sprechen die Ziele dieser Einftihrung, namlich - von den im Laufe des ersten Semesters erworbenen mathematischen Kenntnissen auszugehen -Riemann-Stieltjes-Integrale tiber Intervallen an den Anfang zu stell en und gerade so weit zu entwickeln, wie sie nach wie vor von Nutzen sind, mit beliebigen Verteilungsfunktionen als Integratoren, und unter EinschluB n von Kurvenintegralen im R -davon unabhangig dann das Lebesgue-Integral tiber allgemeinen MaB- raumen aufzubauen, wobei im Zweifel stets der handlicheren, wenn auch etwas spezielleren Formulierung vor maBtheoretischen Verfeinerungen der Vorzug gegeben wurde -schlieBlich die Theorie auch anzuwenden. Ais Anwendungen werden solche Themenkreise der Analysis behandelt, die einerseits von grundsatzlichem eigenen Interesse sind, und wo anderer- seits ein flexibler Integralbegriff unentbehrlich ist. Hierzu gehort ein Pa- ragraph iiber Fouriertransformation auf dem Rn, dann eine ausfiihrliche Behandlung der auf Faltung mit glatten Funktionen beruhenden Reich- haltigkeitssatze fiir Testfunktionen in Verbindung mit den Grundideen der Distributionentheorie, aber auch, als Beispiel fiir die Kraft von Hil- bertraumschliissen und damit fur die Bedeutung der Vollstandigkeit des 2 Raumes L (, ), ein Beweis des Radon-Nikodym'schen Satzes iiber die Exi- stenz von Dichten.


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Product Details
  • ISBN-13: 9783519020783
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Edition: 1987 ed.
  • Language: German
  • Returnable: N
  • Spine Width: 8 mm
  • Weight: 181 gr
  • ISBN-10: 3519020785
  • Publisher Date: 01 Jan 1987
  • Binding: Paperback
  • Height: 216 mm
  • No of Pages: 145
  • Series Title: Teubner Studienbücher Mathematik
  • Sub Title: Eine Einführung in Die Integrationstheorie Und Ihre Anwendungen
  • Width: 140 mm


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