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Sep 2, 2013 at 9:33 comment added YCor A necessary condition is that there exists on $G/H$ an invariant Radon measure, or equivalently that the modular function of $G$ extends that of $H$. (For instance this fails if $G$ is unimodular but not $H$, e.g. upper triangular matrices in $SL_{n\ge 2}(\mathbf{R})$)
Sep 1, 2013 at 17:44 history asked user23860 CC BY-SA 3.0