Reduced distribution function

context

$\rho$ … Classical probability density function

range

$N \equiv \mathrm{dim}(\mathcal M)$

$s < N$

definiendum

$\bar f_s(q^1,p_1,q^2,p_2,\dots,q^s,p_s):=\int\ \rho\ \ \mathrm d q^{s+1} \mathrm d p_{s+1}\cdots \mathrm d q^N \mathrm d p_N$

We also set $f_N:=\rho$ , but that's just introduction of different notation.