Speically, how to calculate the volume of the set $\{(|\langle\psi|M_1|\psi\rangle|^2,...,|\langle\psi|M_s|\psi\rangle|^2)|\rho \in \mathbb{H}^n\}$ in the space $\mathbb{R}^{s}$, in which $\mathbb{H}^n$ is the set of all $n$-qubit pure states, and $\{M_i\}$ is a set of $s$ Hermitian matrices?
I think it might be the integration \begin{align} &\int_{\text{the set}} d|\langle\psi|M_1|\psi\rangle|^2...d|\langle\psi|M_s|\psi\rangle|^2,\\ =&\int_{\mathbb{H}^n} F(\psi,M_1,...,M_s) d\psi, \end{align} but I really don't know what's the function $F$ here.
