General Topology, Measure Theory and Integration

Welcome

This condensed note is designed to mark the key concepts and tools in real analysis, as this is the basis for probability theory. The note is mainly drawn from Chapter 2-5 of the book “Real Analysis and Probability” by R. M. Dudley; more examples and insights from other books will be referenced to help with self-studying.

The reader will understand basic general topology concepts, how measures are constructed, the notion of Lebesgue integration, convergence theorems and \(L^p\) spaces.