Maß und Integral: Lebesgue-Integration für Analysis und Stochastik

René L. Schilling

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Maß und Integral

Lebesgue-Integration für Analysis und Stochastik

René L. Schilling

Language: German

Published/Copyright: 2025

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De Gruyter Studium

About this book

Many areas of mathematics and its applications in physics, economics and computer science require solid knowledge of measure theory. This textbook provides a quick, reliable, and precise guide to the most important results of measure theory.

Überarbeitete und erweiterte Neuauflage
Für Studierende der Mathematik, Physik, Wirtschaftswissenschaften und Informatik
Als Grundlage für eine Vorlesung sowie zum Selbststudium

Author / Editor information

René Schilling is professor of probability theory at Technische Universität Dresden (since 2007). Before he held teaching and research positions at the University of Marburg (Professor, 2004-2007), the University of Sussex Brighton (lecturer/senior lecturer 2000-2004), the Nottingham Trent University (lecturer 1998-2000), from 1994-1998 he was Postdoc at the University of Erlangen, the University of Warwick and the MPI for Mathematics in the Sciences Leipzig. His research focuses on stochastic analysis and the theory of stochastic processes.

Reviews

"Das Werk eignet sich gut für ein hinreichend gründliches Studium der notwendigen Grundlagen, derer es für ein weiter gehendes Studium bedarf."
Philipp Kastendieck in: ekz-Informationsdienst 30/2015

Topics

Frontmatter Publicly Available Download PDF	I
Vorwort Publicly Available Download PDF	V
Abhängigkeit der einzelnen Kapitel Publicly Available Download PDF	VII
Bezeichnungen Publicly Available Download PDF	VIII
Inhalt Publicly Available Download PDF	IX
1 Einleitung Requires Authentication Unlicensed Licensed	1
2 Sigma-Algebren Requires Authentication Unlicensed Licensed	4
3 Maße Requires Authentication Unlicensed Licensed	10
4 Eindeutigkeit von Maßen Requires Authentication Unlicensed Licensed	16
5 Existenz von Maßen Requires Authentication Unlicensed Licensed	22
6 Messbare Abbildungen Requires Authentication Unlicensed Licensed	31
7 Messbare Funktionen Requires Authentication Unlicensed Licensed	37
8 Das Integral positiver messbarer Funktionen Requires Authentication Unlicensed Licensed	45
9 Das Integral messbarer Funktionen Requires Authentication Unlicensed Licensed	52
10 Nullmengen Requires Authentication Unlicensed Licensed	58
11 Konvergenzsätze Requires Authentication Unlicensed Licensed	65
12 Parameter-Integrale Requires Authentication Unlicensed Licensed	70
13 Riemann vs. Lebesgue Requires Authentication Unlicensed Licensed	75
14 Die Räume L^p und L^p Requires Authentication Unlicensed Licensed	80
15 Produktmaße Requires Authentication Unlicensed Licensed	90
16 Der Satz von Fubini–Tonelli Requires Authentication Unlicensed Licensed	96
17 Unendliche Produkte Requires Authentication Unlicensed Licensed	105
18 Der Kolmogorovsche Erweiterungssatz Requires Authentication Unlicensed Licensed	110
19 Bildintegrale und Faltung Requires Authentication Unlicensed Licensed	116
20 Der Satz von Radon–Nikodým Requires Authentication Unlicensed Licensed	123
21 Der allgemeine Transformationssatz Requires Authentication Unlicensed Licensed	134
22 Maßbestimmende Familien Requires Authentication Unlicensed Licensed	146
23 Die Fouriertransformation Requires Authentication Unlicensed Licensed	151
24 Dichte Teilmengen in L^p (1 ⩽ p < ∞) Requires Authentication Unlicensed Licensed	166
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Literatur Requires Authentication Unlicensed Licensed	215
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Publishing information

Pages and Images/Illustrations in book

eBook published on:

November 4, 2024

eBook ISBN:

9783111342894

Paperback published on:

November 4, 2024

Paperback ISBN:

9783111342771

Edition:

2., überarbeitete und ergänzte Auflage.

Pages and Images/Illustrations in book

Front matter:

12

Main content:

220

Illustrations:

19

https://doi.org/10.1515/9783111342894

eBook ISBN: 9783111342894

Paperback ISBN: 9783111342771

Keywords for this book

Probability theory; integration theory; random variables; measure theory

Audience(s) for this book

Students of mathematics, physics, economics, and computer science; lecturers; libraries

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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

Maß und Integral

Overview

About this book

Author / Editor information

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Topics

Table of contents

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