ity measure on G ∗ such that for any set ψ$_{1}$, ...ψ$_{m}$ ∈ G the random vectors (( b, ψ$_{1}$ ) , ... ( b, ψ$_{m}$ )) have the same distribution as for some random functional ˜ b, (( ˜ b, ψ$_{1}$ ) ... ( ˜ b, ψ$_{m}$ )) . An example is a generalized Gaussian process b, so de- fined if for any ψ$_{1}$, ..., ψ$_{m}$ the joint distribution of ( b, ψ$_{1}$ ) , ..., ( b, ψ$_{m}$ ) is Gaus- sian. A generalized Gaussian process is uniquely determined by its mean functional, µ$_{b}$ : ( µ$_{b}$, ψ ) = E ( b, ψ ) , and the covariance bilinear functional, B$_{b}$ ( ψ$_{i}$, ψ$_{j}$ ) = E (( b, ψ$_{i}$ ) ( b, ψ$_{j}$ ) ) . Gelfand, Vilenkin (v.4, p. 260) give the covariance functional of the generalized derivative, W $^{′}$, of the Wiener process as where the overbar represents complex conjugation; for real-valued processes it is not needed. The Fourier transform of a Gaussian random process b is also a Gaussian random process with covariance functional So for F t ( W $^{′}$) the covariance functional is The mean functional is zero for W ′ and F t ( W $^{′}$) . Gelfand and Vilenkin (1964) provide definitions and results for general- B$_{Ft}$$_{(}$$_{b}$$_{)}$ ( ψ$_{i}$, ψ$_{j}$ ) = E (( b, F t ( ψ$_{i}$ )) ( b, F t ( ψ$_{j}$ ) ) ) . B$_{Ft}$$_{(}$$_{W}$ ′ $_{)}$( ψ$_{1}$, ψ$_{2}$ ) = ∫ ∞ 0 F t ( ψ$_{1}$ )( ζ ) F t ( ψ$_{2}$ )( ζ ) dζ. B$_{W}$ ′ ( ψ$_{1}$, ψ$_{2}$ ) = ∫ ∞ 0 ψ$_{1}$ ( t ) ψ$_{2}$ ( t ) dt 46