  Let $\Gamma$ be a Zariski dense Anosov subgroup of a connected semisimple
real algebraic group $G$. For a maximal horospherical subgroup $N$ of $G$, we
show that the space of all non-trivial $NM$-invariant ergodic and
$A$-quasi-invariant Radon measures on $\Gamma \backslash G$, up to
proportionality, is homeomorphic to ${\mathbb R}^{\text{rank}\,G-1}$, where $A$
is a maximal real split torus and $M$ is a maximal compact subgroup which
normalizes $N$. One of the main ingredients is to establish the $NM$-ergodicity
of all Burger-Roblin measures.
