This is a third-year (Semester 5) fundamental course in Measure and Integration Theory.
The primary objective is to introduce students to a powerful and general framework for integration that extends beyond the classical Riemann integral. The core of the course is Lebesgue integration, developed within the context of measured spaces.
Students will learn about sigma-algebras, measures, and measurable functions, which form the foundation for modern probability theory and advanced analysis. The course covers key convergence theorems, such as the Monotone Convergence Theorem and the Lebesgue Dominated Convergence Theorem, which are essential tools for analysis. It also introduces the Fubini Theorem for integrating over product spaces.
This theory is crucial for a deep understanding of areas like functional analysis, probability, and partial differential equations. Prerequisites include Algebra and Topology.
- Course creator: Nabil Khelfallah