[Math 6110] Real analysis

The graduate core course in analysis at Cornell.

Course textbook: Real Analysis: Measure Theory, Integration and Hilbert Spaces.

Recitation covered applications or extensions of material from class. Some topics:

• Hahn-Banach, Convex Duality (Brezis; Functional Analysis, Sobolev Spaces and Partial Differential Equations § 1)
• Almost Every Number is Normal via probability (Kac; Statistical Independence in Probability, Analysis, and Number Theory § 1-2)
• Jordan measure decomposition & Radon-Nikodym
• Some applications of Jensen’s inequality
• (L^p)^* = L^q, and how a weakly-convergent sequence can fail to converge strongly (Lieb & Loss; Analysis § 2)
• Basic L² theory for Δu = f (Krylov; Lectures on Elliptic and Parabolic Equations in Sobolev Spaces § 1)