Measure and Integral

2015
ISBN: 978-3-319-15364-3
Verlag: Springer International Publishing

Buch, Englisch, 172 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2818 g

Reihe: Compact Textbooks in Mathematics

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Kersting, Götz

Brokate, Martin

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

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.

Über Autor(innen)

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.