Measure and Integral

by Martin Brokate, Götz Kersting

Overview

The Lebesgue integral is an essential tool in the fields of analysis and shastics and for this reason, in many areas where mathematics is applied. This textbook is a concise, lecture-tested introduction to measure and integration theory. It addresses the important topics of this theory and presents additional results which establish connections to other areas of mathematics. The arrangement of the material should allow the adoption of this textbook in differently composed Bachelor programmes.

Product Details

ISBN-13:	9783319153643
Publisher:	Springer International Publishing
Publication date:	06/25/2015
Series:	Compact Textbooks in Mathematics
Edition description:	2015
Pages:	172
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Martin Brokate is Professor for Mathematical Modelling at TU Munich, Germany. Götz Kersting is Professor for Shastics at the Goethe University in Frankfurt / Main, Germany.

Table of Contents

Preface.- 1 Introduction.- 2 Measurability.- 3 Measures.- 4 The Integral of Nonnegative Functions.- 5 Integrable Functions.- 6 Convergence.- 7 Uniqueness and Regularity of Measures.- 8 Multiple Integrals and Product Measures.- 9 Absolute Continuity.- 10 The Transformation Formula of Jacobi.- 11 Construction of Measures.- 12 Hilbert Spaces.- 13 Banach Spaces.- Literature.