Measure Theory

Softcover Nachdruck of the original 1. Auflage 1994
ISBN: 978-1-4612-6931-1
Verlag: Springer

Buch, Englisch, 212 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 353 g

Reihe: Graduate Texts in Mathematics

This text is unique in accepting probability theory as an essential part of measure theory. Therefore, many examples are taken from probability, and probabilistic concepts such as independence and Markov processes are integrated into the text. Also, more attention than usual is paid to the role of algebras, and the metric defining the distance between sets as the measure of their symmetric difference is exploited more than is customary.

Zielgruppe

Graduate

Autoren/Hrsg.

Doob, J. L.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

0. Conventions and Notation.- I. Operations on Sets.- II. Classes of Subsets of a Space.- III. Set Functions.- IV. Measure Spaces.- V. Measurable Functions.- VI. Integration.- VII. Hilbert Space.- VIII. Convergence of Measure Sequences.- IX. Signed Measures.- X. Measures and Functions of Bounded Variation on R.- XI. Conditional Expectations; Martingale Theory.- Notation.