Measure Theory and Integration

This module aims at giving a solid background on Measure Theory and Lebesgue Integration. Measure generalizes the familiar concepts of lengths, area, and volumes in finite-dimensional Euclidean spaces. The Lebesgue integral is a generalization of the Riemann integral to a large class of functions. The resulting theory is a fundamental tool for advanced studies in many areas of Mathematics, and Mathematical Physics, which is the prime motivation for developing this module. Topics covered in this module are Construction and Properties of Measures in abstract spaces, Measurable functions, and their properties, Construction and properties of Lebesgue integral, Product measures, General set functions, and Transformations and Functions Spaces.