By a Haar measure on a locall compact group (Hausdorff) we mean a positive measure $\mu$ (contains the borel set's) such that
The measure $\mu$ is left invariant
The measure μ is finite on every compact set
Is $\mu$-regular (i.e. outer and inner regular)
1) It can be shown as a consequence of the above properties that $\mu(U) > 0$ for every non-empty open subset $U$.
Why $\mu(U)>0$ if $U$ is open?
Thank you all.