Let G be a Gaussian vector taking its values in a
separable Fréchet space E. We denote by $\gamma$ its law and by
$(H,\Vert\!\cdot\!\Vert)$ its reproducing Hilbert space. Moreover, let X be an
E-valued random vector of law $\mu$.
In the first section, we prove that if $\mu$ is absolutely continuous
relative to $\gamma$, then there exist necessarily a Gaussian
vector $G'$ of
law $\gamma$ and an H-valued random vector Z such that $G' + Z$ has
the law $\mu$ of X. This fact is a direct consequence of
concentration properties of Gaussian vectors and, in some sense, it is an
unexpected achievement of a part of the Cameron--Martin theorem.
¶ In the second section, using the classical Cameron--Martin
theorem and rotation invariance properties of Gaussian probabilities,
we show that, in many situations,
such a condition is sufficient for $\mu$ being absolutely continuous
relative to $\gamma$.