A Gaussian Radon Transform for Banach Spaces
  We develop a Radon transform on Banach spaces using Gaussian measure and prove that if a bounded continuous function on a separable Banach space has zero Gaussian integral over all hyperplanes outside a closed bounded convex set in the Hilbert space corresponding to the Gaussian measure then the function is zero outside this set. 
Irina Holmes and Ambar N. Sengupta
math.PR math.FA