= Solution
A <Gaussian measure> $\mu$ on a real separable <Banach space> $X$ is a <Borel measure>[Borel probability measure] such that $\ell_*\mu$ is a one-dimensional <normal distribution> for every <continuous linear functional> $\ell\in X^*$. Its mean $m\in X$ and <covariance operator of a Gaussian measure> $C:X^*\to X$ are characterized by
$$
\ell(m)=\int_X\ell(u)\,d\mu(u),
$$
and
$$
\ell_2(C\ell_1)
=\int_X\ell_1(u-m)\ell_2(u-m)\,d\mu(u)
$$
for all $\ell_1,\ell_2\in X^*$.
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