Lebesgue Measure

Definition

A Measure on Borel Sigma-Field, which is a unique extension of function $\tilde{m}:\mathcal{A}\to [0,\infty ]$ on a Semiring $\mathcal{A}=\{(a,b]:a,b\in \mathbb{R},a<b\}$ by Caratheodory Extension Theorem