MATH-GA.2430-001 Real Variables (One-Term)

3 points

Course Description

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.

Prerequisites

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.

Recent Offerings

TBA

Sample Exams

TBA

Recommended Texts

  •  'Real Analysis' by Stein and Shakarchi
  • “Real Analysis” by Royden and Fitzpatrick