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Let X,, • • •, Xn be independent, identically distributed random vectors with values in ]Rd and with a common probability density f. If Vk(x) is the volume o f the smallest sphere centered at x and containing at least k of the Xi, • • •, Xn then fn(x) = k/(nVk (x)) is a nearest neighbor density estimate off. We show that if k = k(n) satisfies k(n)/n --~ 0 and k(n)/log n --* 00 then 51 x I fn(x) f(x)J --~ 0 w .p . l when f is uniformly continuous on Rd .

Note: Addendum to "The Strong Uniform Consistency of Nearest Neighbor Density Estimates"