Real Analysis I

Department: 
MATH
Course Number: 
6337
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every spring and fall semesters

Measure and integration theory

Prerequisites: 

MATH 4318 or consent of the School

Course Text: 

At the level of Folland, Real Analysis

Topic Outline: 
  • Measures: sigma-algebras, measures, outer measures (on abstract measure spaces), Borel measures on IR^n
  • Integration: Measurable functions, integrals, monotone convergence theorem, Fatou's lemma, dominated convergence theorem, Fubini's theorem (on abstract spaces), Lebesgue integral on IR^n
  • Decomposition and differentiation of measures: Signed measures, Lebesgue-Radon-Nikodym theorem, functions of bounded variation