MAT 332E - Real Analysis I

Course Objectives

To introduce the measure of plane sets first, and THEN the measure in general.
To introduce the Lebesgue integral AS extension of the Riemann integral.
To teach properties of Lebesgue integral and give ability to apply on mathematical problems.

Course Description

The concept of measure. Measurable sets on plane and R^n. Inner and outer measure functions. General measure. The extension of measure function. Properties of measurable sets. Cantor and Borel sets. Measurable functions. Lebesgue's integral. The properties of Lebesgue's integral. The notions of convergence. Comparison of Lebesgue's with Riemann's integral. The theorems of Lebesgue, Fatou and Levi. The measure of product. Lebesgue's integral on product spaces. Fubini's theorem.