In [2] (∞-p)-form on a k-th Sobolev space Wk(X), X a compact (spin) manifold, was defined by using Sobolev duality. Integrals of (∞-p)-form on an (∞-p)-form on a cube in Wk(X) were defined without using measure. We show when the lenghth of sides of the cube tends to ∞, infinite dimensional Gaussian integral that is principal on application converges if and only if the cube is imbedded in Wk(X), k<-d+1/2.
A Remark on Infinite Dimensional Gaussian Integral in a Sobolev Space
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