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X is called a white noise on [0,1]. Example 2. Gauss random measures and general white noises. Let m be a cr-finite measure on a measurable space (S, 98(S)) such that L2(S, m) is separable, and let If m\&—»L2(ft) satisfies the following conditions: (i) {M(F)}F is a Gaussian system with mean 0, (ii) E(M(Ft)M(F2)) = m (F! n F2), then M = {M(F}} is called a Gauss random measure with variance measure m. These conditions imply that if {Fn}<^& is a countable disjoint family, then {M(FJ} is independent and M induces a linear random functional on E: = L2(S, p): (Wiener integral).

Suppose that E(X(ff)^cp(f)2 and p

P). Using (9), we obtain or Hence, if E(||L||2)