Let G be a Gaussian vector taking its values in a locally convex separable Fréchet space E. We denote by γ its law and by (H,‖·‖) its reproducing Hilbert space. Let moreover X be an E-valued random vector of law μ. We prove that if μ is absolutely continuous relatively to γ, then there exist necessarly a Gaussian vector G′ of the law γ and an H-valued random vector Z such that G′+Z has the law μ of X. This fact is a direct consequence of isoperimetric properties of Gaussian vector. We show that in many situations, such condition is sufficient for μ being absolutely continuous relatively to γ, using classical Cameron–Martin theorem and invariance properties of Gaussian measures.