Introduction

This Chapter introduce the notion of measure. From the definition on a \(\sigma\)-algebra it goes forward to measure defined on simpler class of sets such as "Lebesgue/Stieljes" measure. How to extend those measures to larger class of sets such as ring. It finishes with Carathéodory's extension theorem that allows to extend those meaningfull measures to the \(\sigma\)-algebra.

• Measures
• From Semi-Ring to Ring
• From Ring to \(\sigma\)-Alegebra: Carathéodory's Extension Theorem