Maß und Integral: Eine Einführung für Bachelor-Studenten

René L. Schilling

Published by De Gruyter 2015

Maß und Integral

Eine Einführung für Bachelor-Studenten

Measure & Integral: An Introduction for Undergraduate Students

René L. Schilling

In the series De Gruyter Studium

https://doi.org/10.1515/9783110350647

Overview
Contents

About this book

Many areas of mathematics and their application in physics, economics, and computer science require a firm grasp of measure theory. This textbook provides a concise, reliable, and accurate introduction to the most important elements of measure theory.

Succinct and precise
Numerous examples and exercises
For students of mathematics, physics, business science, and informatics
Excellent foundation for lectures or self-study

Author / Editor information

René Schilling, Technische Universität Dresden.

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 Requires Authentication Unlicensed Licensed Download PDF	v
Mathematische Grundlagen Requires Authentication Unlicensed Licensed Download PDF	vi
Abhängigkeit der einzelnen Kapitel Requires Authentication Unlicensed Licensed Download PDF	vii
Bezeichnungen Requires Authentication Unlicensed Licensed Download PDF	viii
Inhalt Publicly Available Download PDF	ix
1 Einleitung Requires Authentication Unlicensed Licensed Download PDF	1
2 Sigma-Algebren Requires Authentication Unlicensed Licensed Download PDF	4
3 Maße Requires Authentication Unlicensed Licensed Download PDF	9
4 Eindeutigkeit von Maßen Requires Authentication Unlicensed Licensed Download PDF	14
5 Existenz von Maßen Requires Authentication Unlicensed Licensed Download PDF	20
6 Messbare Abbildungen Requires Authentication Unlicensed Licensed Download PDF	28
7 Messbare Funktionen Requires Authentication Unlicensed Licensed Download PDF	33
8 Das Integral positiver Funktionen Requires Authentication Unlicensed Licensed Download PDF	40
9 Das Integral messbarer Funktionen Requires Authentication Unlicensed Licensed Download PDF	47
10 Nullmengen Requires Authentication Unlicensed Licensed Download PDF	52
11 Konvergenzsätze Requires Authentication Unlicensed Licensed Download PDF	55
12 Parameter-Integrale Requires Authentication Unlicensed Licensed Download PDF	59
13 Riemann vs. Lebesgue Requires Authentication Unlicensed Licensed Download PDF	63
14 Die Räume ℒ_p und L^p Requires Authentication Unlicensed Licensed Download PDF	67
15 Produktmaße Requires Authentication Unlicensed Licensed Download PDF	76
16 Der Satz von Fubini–Tonelli Requires Authentication Unlicensed Licensed Download PDF	81
17 ♦ Unendliche Produkte Requires Authentication Unlicensed Licensed Download PDF	89
18 Bildintegrale und Faltung Requires Authentication Unlicensed Licensed Download PDF	93
19 Der Satz von Radon–Nikodým Requires Authentication Unlicensed Licensed Download PDF	99
20 ♦ Der allgemeine Transformationssatz Requires Authentication Unlicensed Licensed Download PDF	104
21 ♦ Maßbestimmende Familien Requires Authentication Unlicensed Licensed Download PDF	116
22 ♦ Die Fouriertransformation Requires Authentication Unlicensed Licensed Download PDF	120
23 ♦ Dichte Teilmengen in L^p (1 ≤ p < ∞) Requires Authentication Unlicensed Licensed Download PDF	134
24 ♦ Die Rieszschen Darstellungssätze Requires Authentication Unlicensed Licensed Download PDF	140
25 ♦ Konvergenz von Maßen Requires Authentication Unlicensed Licensed Download PDF	151
A Anhang Requires Authentication Unlicensed Licensed Download PDF	159
Literatur Requires Authentication Unlicensed Licensed Download PDF	168
Stichwortverzeichnis Requires Authentication Unlicensed Licensed Download PDF	169

(Deutsch)

Language: German
Publisher: De Gruyter
Audience: Students of mathematics, physics, economics, and computer science, instructors, libraries
Pages
- Front matter: 10
- Main content: 172
Illustrations
- Illustrations: 20
- Tables: 5
Keywords: Measure theory; textbook

eBook

Published: May 19, 2015
ISBN: 9783110350647

Paperback

Published: May 19, 2015
ISBN: 9783110348149