Real Analysis

Catalog description

Legesgue measure theory. Measurable sets and measurable functions. Legesgue integration, convergence theorems. Lp spaces. Decomposition and differentiation of measures. Convolutions. The Fourier transform. MATH 501 Real Analysis I (3) This course develops Lebesgue measure and integration theory. This is a centerpiece of modern analysis, providing a key tool in many areas of pure and applied mathematics. The course covers the following topics: Lebesgue measure theory, measurable sets and measurable functions, Lebesgue integration, convergence theorems, Lp spaces, decomposition and differentiation of measures, convolutions, the Fourier transform.