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

Invariant measures for horospherical actions and Anosov groups