Convergence of Empirical Measures for i.i.d. samples in $W^{-\alpha ,p}$

Gautam Iyer, Raghavendra Venkatraman

Given $N$ i.i.d. samples from a probability measure $\mu$ on ${\mathbf{R}}^d$, we study the rate of convergence of the empirical measure ${\mu }_N\to \mu$ in the negative Sobolev space $W^{-…