Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modeling, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework.

Klappentext

This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.

Inhalt

1. Motivation and preliminaries.- 2. Measure.- 3. Measurable functions.- 4. Integral.- 5. Spaces of integrable functions.- 6. Product measures.- 7. Limit theorems.- 8. Solutions to exercises.- 9. Appendix.- References.