It is proved that, for h measurable and symmetric in its arguments and
X(i) i.i.d., if the sequence (n(-m/2)SIGMA(i1,...,im less-than-or-equ
al-to n, ij not-equal ik if j not-equal k) h(X(i1),...,X(im))}n=1infin
ity is stochastically bounded, then Eh2 < infinity and Eh(X1,x2,...,x(
m)) = 0 a.s..