Classical ensemble expectation value

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	$\langle F\rangle:=\int_{\Gamma_{\mathcal M}}\ F\cdot\rho\ \mathrm d\Gamma$

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