Let $G$ be a locally compact Hausdorff topological group. Then there exists a nonzero Radon measure $\mu$ on $G$ (called a **left Haar measure**) satisfying \begin{align*} \mu(gE) = \mu(E) \quad \text{for all } g \in G \text{ and all Borel sets } E \subset G. \end{align*} Moreover, $\mu$ is unique up to multiplication by a positive constant: if $\nu$ is another left Haar measure, then $\nu = c \mu$ for some $c > 0$.