tags:definition |analysis

Abstract Measure

Statements

Definition. (@Sal08, Definition B.2, @KS04). Let $(X,\mathfrak{S}$) be a measurable space $\mathfrak{S}$. A function $\mu :X\to {\mathbb{R}}_{\ge 0}$ is said to be a measure if

1. The equality $\mu (\varnothing )=0$ holds.
2. It is countably additive.