Measure and Integral

The Lebesgue integral is an essential tool in the fields of analysis and stochastics 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.

New arrangement of the subject matter with hands-on examples Concise presentation of the material Provides guidance and material for different variants of 2-hour courses Focuses on the essentials of measure and integration theory Includes supplementary material: sn.pub/extras

Autorentext

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

Inhalt
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.