Integration Theory: 1st Edition (Hardback) book cover

Integration Theory

1st Edition

By Wolfgang Filter, K. Weber

Chapman and Hall/CRC

296 pages

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Hardback: 9780412576805
pub: 1997-07-01
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Description

This introductory text acts as a singular resource for undergraduates learning the fundamental principles and applications of integration theory.

Chapters discuss: function spaces and functionals, extension of Daniell spaces, measures of Hausdorff spaces, spaces of measures, elements of the theory of real functions on R.

Table of Contents

Introduction

Function Spaces and Functionals

Ordered Sets, Lattices

The Spaces RX and R-X

Vector Lattices of Functions

Functionals

Daniell Spaces

The Extension of Daniell Spaces

Upper Functions

Lower Functions

The Closure of (x, L, I)

Convergence of Theorems in (x, L(L), I)

Examples

Null Functions and Null Sets, Integrability

Examples

The Induction Principle

Summary

Measure and Integral

The Extension of Positive Measure Spaces

Examples

Locally Integrable Functions

Product Measures

Fubini's Theorem

Measures of Hausdorff Spaces

Lp-Spaces

Vector Lattices, Lp-Spaces

Spaces of Measures

The Vector Lattice Structure

The Variation

Hahn's Theorem

Absolute Continuity

The Radon-Nikodym Theorem

Elements of the Theory of Real Functions on R

Functions of Locally Finite Variation

Absolutely Continuous Functions

About the Series

Chapman Hall/CRC Mathematics Series

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Subject Categories

BISAC Subject Codes/Headings:
MAT007000
MATHEMATICS / Differential Equations