Concerning a Kind of Integrals of Cinmplex-Valued Functions of Large Numbers

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Concerning a Kind of integrals of Complex-ValnedFunctions of Large Nnmbers

Here presented are two limit theorems for a kind of integrals involvingcomplex-valued functions of large numbers. The form of integrals may be regardedas a natural generalization of those integrals occured in the probability limit theoremsof Chung and Erds. Our main result is Theorem 2 whose Proof rests upon some knownresults of 1] and makes an extentive use of Bonnet's second mean value theorem andrelated analytic techniques.