# Measure and Integration: Course Contents (MAT 452)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

## Course Objective

## Course Contents (MAT 452)

- Definition and examples of algebras and s-algebras,
- Basic properties of measurable spaces, Definition and examples of measure spaces, Outer measure,
- Lebesgue measure, Measurable sets, Complete measure spaces, Some equivalent formulations of measurable functions, Examples of measurable functions, Various characterization of measurable functions,
- Property that holds almost everywhere, Egorov’s theorem,
- Definition of Lebesgue integral, Basic properties of Lebesgue integrals,
- Comparison between Riemann integration and Lebesgue integration, L
^{2}-space, - The Riesz-Fischer theorem.