An introduction to measure-theoretic probability
This book provides in a concise, yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in statistics, probability and other related areas, should be equipped with. The approach is classical, avoiding the use of mathematical tools not necessary for carrying out the discussions. All proofs are presented in full detail.* Excellent exposition marked by a clear, coherent and logical development of the subject* Easy to understand, detailed discussion of material* Complete proofs
1 ressource en ligne (xviii, 443 pages) : illustrations.
9780080575308, 0080575307
1097309666
Front Cover; An Introduction to Measure-Theoretic Probability; Copyright Page; TABLE OF CONTENTS; PREFACE; CHAPTER 1. Certain Classes of Sets, Measurability, and Pointwise Approximation; 1. Measurable spaces; 2. Product measurable spaces; 3. Measurable functions and random variables; Exercises; CHAPTER 2. Definition and Construction of a Measure and Its Basic Properties; 1. About measures in general, and probability measures in particular; 2. Outer measures; 3. The Carathéodory extension theorem; 4. Measures and (point) functions; Exercises