Parabolic reduction for volumes and semistable masses

Let $G$ be a split reductive group over a number field $F$, let $B/F$ be a fixed Borel subgroup, and let $P=UM$ be a standard parabolic subgroup with Levi factor $M$. If $M=\prod_i M_i$ is its decomposition into simple factors, define

$$\nu_P:=\prod_i\operatorname{Vol}\Big(\mathbb K_{M_i}Z_{M_i^1(\mathbb A)}\backslash M_i^1(\mathbb A)\big/M_i(F)\Big),$$

and

$$\mu_P:=\prod_i\operatorname{Vol}\Big(\mathbb K_{M_i}Z_{M_i^1(\mathbb A)}\backslash M_i^1(\mathbb A)^{\mathrm{ss}}\big/M_i(F)\Big).$$

Here $\nu_G$ and $\mu_G$ denote the corresponding invariants for $G$, and $\operatorname{sgn}(P)$ denotes the sign of $P$. Parabolic reduction. For every standard parabolic subgroup $P$ of $G$, there exist constants $c_P\in\mathbb Q$ and $e_P\in\mathbb Q_{>0}$ such that

$$\nu_G=\sum_P c_P\cdot\nu_P,\qquad \mu_G=\sum_P\operatorname{sgn}(P)e_P\cdot\nu_P.$$

The assertion proposes that the volume and semistable mass of a reductive group decompose into contributions from its standard parabolic subgroups. The source gives no resolution evidence.