Fall 2016 MATH 202A 001 LEC

Introduction to Topology and Analysis
001 LECMoWeFr 1:00PM - 1:59PMEvans 60Francis Christ18984
UnitsEnrollment Status
Additional Information: 

Prerequisites: 104. 110, 113, and 185 are strongly recommended.

Syllabus: Brief introduction to metric spaces.Measures (sigma--algebras, outer measures, Borel measures). Lebesgue integration. Integrals and limits (Monotone and Dominated Convergence theorems; Fatou's lemma). Signed measures, and differentiation of measures (Radon-Nikodym theorem,Lebesgue's differentiation theorem). Functions of bounded variation. Point set topology (metric spaces, completion, topological spaces, compactness, separation properties, local compactness, Weierstrass and Stone-Weierstrass theorems, Tychonoff product theorem). As time permits: Baire's theorem. Product measures. L^p spaces (completeness and the Holder and Minkowski inequalities, duality).

Office: 809 Evans Hall.

Required Text: Real Analysis (2nd edition) by Gerald B. Folland.

Please see more detailed announcement at https://math.berkeley.edu/~mchrist/Courses/202Aannounce.pdf .