Gauss Measure

The standard Gauss measure of a finite dimensional Real Hilbert Space $H$ with norm $\vert\vert\cdot\vert\vert _H$ has the Borel Measure

$$\mu_H\,(dh)=(\sqrt{2\pi}\,)^{-{\rm dim}(H)}\mathop{\rm exp}\... ...xtstyle{1\over 2}}\vert\vert h\vert\vert^2_H)\lambda_H \,(dh),$$

where $\lambda_H$ is the Lebesgue Measure on $H$.