Rieszsche Darstellungssatz und ausgewählte Anwendungen
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Rieszsche Darstellungssatz und ausgewählte Anwendungen

Rieszsche Darstellungssatz und ausgewählte Anwendungen


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About the Book

Diplomarbeit aus dem Jahr 2011 im Fachbereich Mathematik - Analysis, Note: 1.7, Katholische Universität Eichstätt-Ingolstadt, Sprache: Deutsch, Abstract: Bevor in den konkreten Inhalt dieser Arbeit eingestiegen werden soll, sei hier in aller Kürze eine Vorbemerkung zum Umgang mit und Verständnis der Arbeit gegeben, um möglichen späteren Ungereimtheiten gleich am Anfang vorzubeugen. Vier grundlegende Festlegungen In der vorliegenden Arbeit werden die meisten Deklarationen an der Stelle des ersten Gebrauchs vorgenommen, einige jedoch seien hier vorangestellt. 1 Die Teilmenge aller Punkte x einer nichtleeren Menge X, auf die eine bestimmte Eigenschaft P zutrifft wird im Folgenden, wenn es offensichtlich ist, dass es sich um eine Teilmenge von X handelt, durch fx: P trifft auf x zug dargestellt. Die Menge X selber wird in dieser Notation nicht mehr erwähnt. Wird eine auf einem topologischen Raum X definierte, in einen topologischen Raum Y abbildende Funktion f als stetig bezeichnet, so ist immer globale Stetigkeit gemeint, d.h. für offene Mengen U Y gilt, dass das Urbild dieser Mengen unter f (bezeichnet durch f-1(U)) offen in X ist. Sei (X;M) ein Maßraum (M eine sigma-Algebra über einer nichtleeren Menge X)2 und Y ein topologischer Raum. In der gesamten Arbeit werden bei der Definition von Integralfunktionen mithilfe eines gegebenen Maßes mü (auf M) und darauf aufbauenden Definitionen zwei bzgl. mü messbare Funktionen f; g: X -> Y als gleich angesehen, wenn sie bezüglich mü fast überall gleich sind. Wenn nicht gesondert darauf hingewiesen wird bei Verwendung der Räume R und C von deren Standardtopologien ausgegangen, d.h. der euklidischen Topologie. [...] 1 Oft gebräuchliche Standardnotationen (wie beispielsweise E für den Abschluss einer Menge E oder Ec für das Komplement etc.) werden ohne extraige Einführung verwendet. Bei Mehrdeutigkeiten und außergewöhnlichen Notationen wird an Ort und Stelle gesondert noch einmal auf die spezielle Bedeutung im jeweiligen Zus


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Product Details
  • ISBN-13: 9783656213222
  • Publisher: Grin Publishing
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 6 mm
  • Width: 148 mm
  • ISBN-10: 3656213224
  • Publisher Date: 10 Jun 2012
  • Height: 210 mm
  • No of Pages: 98
  • Series Title: German
  • Weight: 186 gr


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Rieszsche Darstellungssatz und ausgewählte Anwendungen
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