Measure and Integration
ENSTSA
About This Course
This course provides a rigorous introduction to measure theory and Lebesgue integration. It is designed to extend classical calculus by building a modern analytical framework essential for advanced mathematics, functional analysis, and probability theory.
Target Audience
This course is specifically intended for 2nd Year Preparatory Cycle Students in Mathematics and Science.
Course Structure
Our curriculum is organized into 3 main chapters:
- Chapter 1: Sigma Algebras and Measures
- Chapter 2: Measurable Functions
- Chapter 3: Integration
Course Objectives
By the end of this course, you will be able to:
- Construct the Borel σ-algebra on &mathbb;R.
- Verify the properties of a measure on a given measurable space.
- Distinguish between different types of convergence.
- Apply the Monotone Convergence Theorem in limit-integral problems.
- Apply the Dominated Convergence Theorem in limit-integral problems.
Prerequisites
Before enrolling, students should be familiar with:
- Real Analysis: Limits, continuity, sequences, and basic Riemann integration.
- Linear Algebra: Vector spaces, linear mappings, and the structure of &mathbb;Rn.
- Topology: Open and closed sets, convergence, and metric spaces.