Given a locally compact group $G$ it's a well known fact the "uniqueness" of the left haar measure, i.e. a measure that satisfies $\mu(A)=\mu(xA),\forall x\in G$. }
I want to know what it's known about the space of measures that satisfies $\mu(A)=\mu(xA)$, where $x\in H$ and $H$ a closed subgroup of $G$. Any reference will be very helpful.
Thanks!