Classical ensemble expectation value

Set

 context $\langle \mathcal M, H,\pi,\pi_0,{\hat\rho},{\hat\rho}_0\rangle$ … classical statistical ensemble
 definiendum $\langle \cdot \rangle: (\Gamma_{\mathcal M}\to \mathbb R)\to \mathbb R$ definiendum $\langle F\rangle:=\int_{\Gamma_{\mathcal M}}\ F\cdot\rho\ \mathrm d\Gamma$

Discussion

In the definition we must use $\rho$, i.e. the noramlized ${\hat\rho}$.