A note on weak convergence of the $n$-point motions of Harris flows

In this note we extend the main results of [2] and [8], which concern the weak convergence of the $n$-point motions of smooth Harris flows to those of the Arratia flow, to the case when the covariance functions of these Harris flows converge pointwise to a covariance function whose support is of zero Lebesgue measure.