MATH-GA.2430-001 Real Variables (One-Term)
Measure theory and integration. Lebesgue measure on the line and abstract measure spaces. Absolute continuity, Lebesgue differentiation, and the Radon-Nikodym theorem. Product measures, the Fubini theorem, etc. Lp spaces, Hilbert spaces, and the Riesz representation theorem. Fourier series.
A familiarity with rigorous mathematics, proof writing, and the epsilon-delta approach to analysis, preferably at the level of MATH-GA 1410, 1420 Introduction to Mathematical Analysis I, II.
Note: Master's students need permission of course instructor before registering for this course.
- Folland's Real Analysis: Modern Techniques and Their Applications
- Bass' Real Analysis for Graduate Students