let $\gamma$ be an anosov subgroup of a connected semisimple real linear lie 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 $\mathbb{r}^{\mathrm{rank} (g)-1}$, where $a$ is a maximal real split torus and $m$ is a maximal compact subgroup which normalizes $n$. \\ \\ this is joint work with hee oh.