  We extend the notion of the distance to a measure from Euclidean space to
probability measures on general metric spaces as a way to do topological data
analysis in a way that is robust to noise and outliers. We then give an
efficient way to approximate the sub-level sets of this function by a union of
metric balls and extend previous results on sparse Rips filtrations to this
setting. This robust and efficient approach to topological data analysis is
illustrated with several examples from an implementation.
