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Presented to the Society, September 17, 1945; received by the editors August 14, 1945. P) See for instance Evaluation of various Wiener integrals by use of certain Sturm-LiouvilU differential equations, Bull. Amer. Math. Soc. vol. 51 (1945) pp. 73-90, where further references are given. (*) Whenever convenient we follow the physicists in denoting by R the average (mathematical expectation) of R. We also use the customary symbol E(R).

On the average of a certain Wiener functional and a related limit theorem in calculus of probability