A SIMPLE DEFINITION OF THE FEYNMAN INTEGRAL,WITH APPLICATIONS

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PROOF. By the definition of S , there exists a unique H such that

L2

v b

3

F(x) » f expCi S J v (t)dx.(t)}d*(v) = F*(x) .

Tv 0=1 a J J

Thus F is defined whenever the integral exists, and so F exists s-almost every-

V V

-X- -X -X

where on C [a,b] and everywhere on D [a,b] . Thus F e s and F » F and the Lemma

i s proved.