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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

\begin{displaymath}
\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),
\end{displaymath}

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




© 1996-9 Eric W. Weisstein
1999-05-25