%0 Journal Article %T Laws of large numbers and nearest neighbor distances %A Mathew D. Penrose %A J. E. Yukich %J Mathematics %D 2009 %I arXiv %X We consider the sum of power weighted nearest neighbor distances in a sample of size n from a multivariate density f of possibly unbounded support. We give various criteria guaranteeing that this sum satisfies a law of large numbers for large n, correcting some inaccuracies in the literature on the way. Motivation comes partly from the problem of consistent estimation of certain entropies of f. %U http://arxiv.org/abs/0911.0331v1