Let Xi, i ∈ N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B → R. Under a central limit theorem assumption, an asymptotic evaluation of Zn = E (exp (nΦ(Σni=1 Xi/n))), up to a factor (1 + 0(1)), has been gotten in Bolthausen . In this paper, we show that the same asymptotic evaluation can be gotten without the central limit theorem assumption.
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