ENGLISH

The Lebesgue-Stieltjes Integral: A Practical Introduction

By M. Carter , B. van Brunt

Book information

Publisher
Springer
Year
2000
ISBN
9781402054945, 1402054947
Language
english
Format
PDF
Filesize
13 MB (13701647 bytes)
Series
Undergraduate Texts in Mathematics
Edition
1
Pages
235\235
Topic
Mathematics Algebra
Time added
2010-02-18 13:16:04

Description

Mathematics students generally meet the Riemann integral early in their undergraduate studies, then at advanced undergraduate or graduate level they receive a course on measure and integration dealing with the Lebesgue theory. However, those whose interests lie more in the direction of applied mathematics will in all probability find themselves needing to use the Lebesgue or Lebesgue-Stieltjes Integral without having the necessary theoretical background. It is to such readers that this book is addressed. The authors aim to introduce the Lebesgue-Stieltjes integral on the real line in a natural way as an extension of the Riemann integral. They have tried to make the treatment as practical as possible. The evaluation of Lebesgue-Stieltjes integrals is discussed in detail, as are the key theorems of integral calculus as well as the standard convergence theorems. The book then concludes with a brief discussion of multivariate integrals and surveys ok L^p spaces and some applications. Exercises, which extend and illustrate the theory, and provide practice in techniques, are included.

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