Measure Theory and Probability Theory

• Main Authors: Athreya, Krishna B. (Author), Lahiri, Soumendra N. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2006.
• Series: Springer Texts in Statistics,
• Subjects: Mathematics.; Computers.; Mathematical analysis.; Analysis (Mathematics).; Measure theory.; Operations research.; Management science.; Probabilities.; Statistics.; Probability Theory and Stochastic Processes.; Theory of Computation.; Analysis.; Measure and Integration.; Statistical Theory and Methods.; Operations Research, Management Science.

This is a graduate level textbook on measure theory and probability theory. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. It is intended prima...

Table of Contents:

• Measures and Integration: An Informal Introduction
• Measures
• Integration
• Lp-Spaces
• Differentiation
• Product Measures, Convolutions, and Transforms
• Probability Spaces
• Independence
• Laws of Large Numbers
• Convergence in Distribution
• Characteristic Functions
• Central Limit Theorems
• Conditional Expectation and Conditional Probability
• Discrete Parameter Martingales
• Markov Chains and MCMC
• Stochastic Processes
• Limit Theorems for Dependent Processes
• The Bootstrap
• Branching Processes.