A Primer of Lebesgue Integration / Edition 1

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Overview

The Lebesgue integral is the standard tool for mathematics, physics, and engineering. It is used where sequences or series arise and where one might wish to express the integral of a sum as a sum of integrals or vice versa. It is essential in Fourier analysis and for the construction of Hilbert space. This primer gives a concrete treatment, building Lebesgue theory in a way parallel to the Riemann integral of beginning calculus. It makes the powerful tools of Lebesgue theory readily available to those in applied areas. It is a good introduction for those going on in mathematics and a refresher with new insights for those in the field. H.S. Bear gives a clear and engaging account of this important and previously forbidding piece of mathematics, providing readers with a key to many areas of analysis.

This primer gives a concrete treatment, building Lebesgue theory in a way parallel to the Piemann integral of beginning calculus. It makes the powerful tools of Lebesgue theory readily available to those in applied areas. A good introduction for those going on in mathematics as well as a refresher holding new insights for those in the field.

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Product Details

  • ISBN-13: 9780120839704
  • Publisher: Elsevier Science & Technology Books
  • Publication date: 1/28/1995
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 163
  • Product dimensions: 6.30 (w) x 9.34 (h) x 0.67 (d)

Table of Contents

Preface
1 The Riemann-Darboux Integral 1
2 The Riemann Integral as a Limit of Sums 9
3 Lebesgue Measure on (0,1) 21
4 Measurable Sets - The Caratheodory Characterization 27
5 The Lebesgue Integral for Bounded Functions 43
6 Properties of the Integral 53
7 The Integral of Unbounded Functions 61
8 Differentiation and Integration 73
9 Plane Measure 83
10 The Relationship between [mu] and [lambda] 91
11 General Measures 103
12 Integration for General Measures 111
13 More Integration - the Radon-Nikodym Theorem 119
14 Product Measures 133
15 The Space L[superscript 2] 147
Index 159
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