Measure Integral And Probability

This is a graduate level textbook on measure theory and probability theory. It presents the main concepts and results in measure theory and probability theory in a simple and easy-to-understand way. It further provides heuristic explanations behind the theory to help students see the big picture.

Assuming only calculus and linear algebra, Professor Taylor introduces readers to measure theory and probability, discrete martingales, and weak convergence. This is a technically complete, self-contained and rigorous approach that helps the reader to develop basic skills in analysis and probability.

In 1902 the French mathematician Henri Lebesgue wrote his famous dis- sertation Integrale, Longueur, Aire (Integral, Length and Area). Since 1914 the theory of the Lebesgue measure has become a part of the under- graduate curriculum in analysis in all the technologically advanced coun- tries of the world.