Let G be a connected semisimple real algebraic group and Γ a Zariski dense Anosov subgroup of G with respect to a minimal parabolic subgroup P. Let N be the maximal horospherical subgroup of G given by the unipotent radical of P. We describe the N-ergodic decompositions of all Burger–Roblin measures as well as the A-ergodic decompositions of all Bowen–Margulis–Sullivan measures on ΓG. As a consequence, we obtain the following refinement of the main result of [17]: the space of all non-trivial N-invariant ergodic and P°-quasi-invariant Radon measures on ΓG, up to constant multiples, is homeomorphic to ℝ^{rank G−1} × {1, …, k} where k is the number of P°-minimal subsets in ΓG.

令G为连通半单实代数群，并且 Г 为G相对于最小抛物线子群P的 Zariski 稠密阿诺索夫子群。令N为由P的单能根给出的G的最大星球子群。我们描述了所有 Burger-Roblin 测度的N遍历分解以及所有 Bowen-Margulis-Sullivan 测度对 Γ G的A遍历分解。因此，我们对[17]的主要结果进行了以下细化：所有非平凡的N-不变遍历和P °-准不变Radon测度在ΓG上的空间，直到常数倍，同胚于ℝ^{秩G −1} × {1, …, k } 其中k是Γ G中P °-最小子集的数量。