Measure and Probability Th

Catalog description

Measure and Probability Theory: Concepts such as Lebesgue measure and integration, basic convergence theorems, Lp spaces, Hilbert spaces, Banach spaces, Radon- Nikodym derivative, product spaces, product measures are developed for the study of probability spaces, random variables as measurable functions, modes of probabilistic convergence, expectation, conditional expectations and probability, statistical independence. Basic tools of probability theory are covered, such as characteristic functions, the weak and strong laws of large numbers, the central limit theorem, and martingales.