MATH 8352 Analysis and Measure Theory
This course will introduce fundamental ideas and techniques from analysis and Lebesgue integration. Topics will include Banach spaces, bounded linear operators, fixed point theorems, Hilbert spaces, compact operators, and their spectrum. Topics in Lebesgue integration include outer and inner measures, the Carathéodory theorem, Lebesgue integral, the Lebesgue fundamental theorem of calculus, the Lebesgue multiple integrals, the Fubini–Tonelli theorem, Lebesgue spaces, Young’s inequality, Holder’s inequality, Minkowski’s inequality, and convergence in Lebesgue spaces.
Prerequisite
Consent of Instructor.