It is proved that, for h measurable and symmetric in its arguments and Xᵢ i.i.d., if the sequence -m/2 ∑i₁,…,iₘ≤ n,iⱼ≠ iₖ if j≠ k h(Xi₁,…, Xiₘ)\^∞ₙ₌₁ is stochastically bounded, then Eh² < ∞ and Eh(X₁,x₂,…,xₘ) = 0 a.s.
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Giné et al. (1994) studied this question.
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