## 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