Definition 27.2.1 (Haar Measure).label Let $G$ be a locally compact group and $\mu: \cb_{G} \to [0, \infty]$ be a non-zero Radon measure, then $\mu$ is a left Haar measure if

1. (LH)

   For each $g \in G$ and $A \in \cb_{G}$, $\mu(gA) = \mu(A)$.

and a right Haar measure if

1. (RH)

   For each $g \in G$ and $A \in \cb_{G}$, $\mu(Ag) = \mu(A)$.