640:501 Real Analysis, Fall 2008 homepage
640:501 REAL ANALYSIS, Fall, 2008
MW4 (1:40-3:00), Hill Center, 425
Text: G. Folland, Real Analysis: Modern Techniques and
Their Applications, second edition, Wiley Interscience,
1999. ISBN 0-471-31716-0.
Daniel Ocone; ocone-at-math-dot-rutgers-dot-edu.
Office Hours: Hill 518: W5, or by appointment.
SYLLABUS, NOTES, and PROBLEM SETS
This course assumes familiarity with real analysis at the level,
roughly, of W. Rudin, Principles of Mathematical Analysis.
- Basic real variable function theory, measure and integration theory
prerequisite to pure and applied analysis.
Topics: Riemann and Lebesgue-Stieltjes integration; measure spaces,
measurable functions and measure; Lebesgue measure and integration;
convergence theorems for integrals; Lusin and Egorov theorems;
product measures and Fubini-Tonelli theorem; signed measures,
Radon-Nikodym theorem, and Lebesgue's differentiation theorem.