Definition:Left Haar Measure

Definition
Let $\struct {G, \odot, \tau}$ be a locally compact topological group.

Let $\BB$ be the Borel $\sigma$-algebra.

A measure $m$ on $\BB$ is called a left Haar measure :
 * $(1): \quad \forall U \in \tau : U \ne \O \implies \map m U > 0$
 * $(2): \quad$ $m$ is left translation invariant, that is:
 * $\forall g \in G, \forall E \in \BB : \map m {g \odot E} = \map m E$
 * where:
 * $ g \odot E := \set {g \odot h : h \in E}$