MATH 6410: Foundations of Probability Theory
(Cross-listed with STAT 6410).
Credits: 3. Contact Hours: Lecture 3.
Prereq: MATH 4140 or MATH 5010 or Graduate Classification
Sequences and set theory; Lebesgue measure, measurable functions. Absolute continuity of functions, integrability and the fundamental theorem of Lebesgue integration. General measure spaces, probability measure, extension theorem and construction of Lebesgue-Stieljes measures on Euclidean spaces. Measurable transformations and random variables, induced measures and probability distributions. General integration and expectation, Lp-spaces and integral inequalities. Uniform integrability and absolutecontinuity of measures. Probability densities and the Radon-Nikodym theorem. Product spaces and Fubini-Tonelli theorems.
(Typically Offered: Fall)