Graduate Programs
Graduate Home
Ph D Programs
Masters Degree
Ph D Program Requirements
Course Descriptions
Current Courses
Admissions
Current Graduate Students
Graduate Student Seminar
SIAM Chapter Seminar
Recent Graduates
Incoming Students

Graduate Courses
21720
Measure and Integration
12 units
Prerequisites: knowledge of (undergraduate) real analysis
Description
 Outer measure, measure, algebras, Dynkin
Theorem,
Carathéodory's Extension Theorem
 Borel measures, Lebesgue measure
 Measurable functions, Lebesgue integral (Monotone Convergence
Theorem,
Fatou's Lemma, Dominated Convergence Theorem)
 Modes of Convergence (Egoroff's Theorem, Lusin's Theorem)
 Product Measures (FubiniTonelli Theorems), ndimensional Lebesgue
integral
 Signed Measures (Hahn Decomposition, Jordan Decomposition,
RadonNikodym
Theorem, change of variables)
 Differentiation (Lebesgue Differentiation Theorem)
 Spaces (Hölder's inequality, Minkowskii's inequality,
completeness, equiintegrability (uniform integrability), Vitali's
convergence theorem)
