## Reduced distribution function

### Set

 context $\rho$ … Classical probability density function
 range $N \equiv \mathrm{dim}(\mathcal M)$
 $s < N$
 definiendum $\bar f_s(q^1,p_1,q^2,p_2,\dots,q^s,p_s):=\int\ \rho\ \ \mathrm d q^{s+1} \mathrm d p_{s+1}\cdots \mathrm d q^N \mathrm d p_N$

### Discussion

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