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

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