Correlation function of a point process ($R_k$)

The $k$th correlation function is the density of the $k$th factorial moment measure: integrating a nonnegative test function against $R_k$ gives the expectation of its sum over ordered $k$-tuples of distinct points. For exactly $m$ exchangeably labelled points with symmetric joint density $f_m$, it is $m!/(m-k)!$ times the marginal density of $k$ labels. It is not normalized to have total mass one.