MATH 8353 Measure Theory
The purpose of this course is to present Lebesgue’s theory of integration and its applications. The concept of measure spaces will be introduced, and topics including Carathéodory’s extension theorem, Borel and Lebesgue measures will be covered. The Lebesgue integral and measurable functions will be defined, together with various properties, such as the convergence theorems, Lusin’s theorem and Egorov’s theorem. Further topics will include Fubini’s Theorem, the Radon-Nikodym Theorem, Lebesgue Differentiation Theorem, and L^p spaces. Applications will include Fourier Transforms and their properties.
Prerequisite
Consent of Instructor.
Offered
As scheduled