Abstract for Sfb Preprint No. 317

The Gaussian Measure on Algebraic Varieties I. Agricola and T. Friedrich We prove that the ring R[M] of all polynomials defined on a real algebraic variety M in R^n is dense in the Hilbert space L^2(M,e^{-|x|^2}dM), where dM denotes the volume form of M and e^{-|x|^2}dM the Gaussian measure on M.