On the Gaussian representation of intrinsic volumes

The geometrically based intrinsic volume functionals have figured importantly in Gaussian processes, such as in a remarkable expansion for the Wills functional equation(1)W(K)=Eexp{supt∈K[Xt−(1/2)σt2]},σt=EXt2. Using the Hadwiger Characterization Theorem, we give an alternate proof of the Gaussian representation of intrinsic volumes.