MTH 535 Measure Theory and Integration


Department of Mathematics, University of Rhode Island



Instructor

Orlando Merino, merino@math.uri.edu, 874-4442, Lippitt Hall 101C

Meets

M, W  3 p.m. Lippitt Hall 201

Text

Adams, M. and Guillemin, V., Measure Theory and Probability, latest Edition, Birkauser, Boston,  supplemented by handouts

Prerequisites

MTH 435-436 or permission of the instructor

About the Course

This course is part II of an introduction to real analysis at the graduate level, particularly integration theory and its applications to Fourier analysis, probability theory and other mathematical areas. This course can be regarded as a continuation of MTH 435-436 with the same level of rigor. It should useful to well-prepared students of electrical engineering, physics or statistics as well as students of mathematics. Topics: Hahn decomposition, Lebesgue-Radon-Nikodym theorem, review of metric spaces, L1, L2, Hilbert space, Fourier series, Fourier integrals, applications, invariant measures, Birkhoff Ergodic Theorem, Random variables and stochastic processes, Brownian motion, other topics may be covered depending on interest.

Evaluation

Homework (50%), Midterm Exam (20%), Final Exam (30%)