Then for any integrable test function ϕ, E " 1 N NX i=1 ϕ( ˜X (i)) {(X (j), ˜w(j))}N j=1 # = NX j=1 ˜w(j) ϕ(X (j))

Let { ˜X (i)}N i=1 be obtained by multinomial resampling from P i ˜w(i)δX (i), assigning equal weights 1/N · 1963