Real Analysis (Math 545) - Fall 2020
General Information
Some Remarks on Writing Mathematical Proofs by Jack Lee
Instructor: Vyron Vellis (vvellis "AT" utk "DOT" edu)
Lecture: MWF 9:15 - 10:05 AM in HBB 103 or through Zoom
Syllabus: Syllabus
Office hours: Through Zoom either on TuWTh 4-5 pm or by appointment.
Topics:
Measure theory: positive Borel measures, measurable sets, measurable functions, and Caratheodory's theorem.
Abstract integration: Lebesgue integration, Fatou's lemma, monotone and dominated convergence theorems, Fubini Theorem.
Differentiation: Absolutely continuous functions, Radon-Nykodim theorem and differentiation of measures.
Lp spaces and duality, Hölder, Minkowski and Jensen inequalities.
Functional analysis: Hilbert and Banach spaces, Riesz representation theorem for bounded functionals on L p .
Prerequisite: Familiarity with proof-writing and one year of advanced calculus.
Textbook: R. Bass, Real Analysis for Graduate Students , Version 4.2 (it can be found in Dr. Bass's webpage).