Integration Theory

by K. Weber

Overview

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.

Product Details

ISBN-13:	9781351437776
Publisher:	CRC Press
Publication date:	04/28/2020
Series:	Chapman Hall/CRC Mathematics Series
Sold by:	Barnes & Noble
Format:	eBook
Pages:	296
File size:	2 MB

About the Author

W. Filter Professor of Analysis University of Palermo Italy. K. Weber Professor of Mathematics Technikum Winterthur Switzerland.

Table of Contents

Introduction -- Preface -- Introduction -- 1 Preliminaries -- 2 Function spaces and functionals -- 2.1 Ordered sets and lattices -- 2.2 The spaces RX and X -- 2.3 Vector lattices of functions -- 2.4 Functionals -- 2.5 Daniell spaces -- 3 Extension of Daniell spaces -- 3.1 Upper functions -- 3.2 Lower functions -- 3,3 The closure of (X, £, t) -- 3.4 Convergence theorems for (X, £(t),?) -- 3.5 Examples -- 3.6 Null functions, null sets and integrability -- 3.7 Examples -- 3.8 The induction principle -- 3.9 Functionals on -- 3.10 Summary -- 4 Measure and integral -- 4.1 Extensions of positive measure spaces -- 4.2 Examples -- 4.3 Locally integrable functions -- 4.4 n-measurable functions -- 4.5 Product measures and Fubini’s theorem -- 5 Measures on Hausdorif spaces -- 5.1 Regular measures -- 5.2 Measures on metric and locally compact spaces -- 5.3 The congruence invariance of the n-dimensional Lebesgue measure -- 6 £-spaces -- 6.1 The structure of £.spaces -- 6.2 Uniform integrability -- 7 Vector lattices, L-spaces -- 7.1 Vector lattices -- 7.2 L”-spaces -- 8 Spaces of measures -- 8.1 The vector lattice structure and Hahn’s theorem -- 8.2 Absolute continuity and the Radon-Nikodym theorem -- 9 Elements of the theory of real-valued functions on R -- 9.1 Functions of locally finite variation -- 9.2 Absolutely continuous functions -- Symbol index -- Subject index.