Let $\mu$ be a centred Radon Gaussian measure on a locally convex space $X$ and $q : X \to \mathbb{R}$ a seminorm that is $\mathcal{B}(X)_\mu$-measurable, where $\mathcal{B}(X)_\mu$ is the Lebesgue completion of the Borel $\sigma$-algebra on $X$. Consider a linear functional $\phi : X \to \mathbb{R}$ with $\vert \phi \vert \le q$. Is it also necessarily $\mathcal{B}(X)_\mu$-measurable?

It follows from theorem 2.10.11 in Bogachev's monograph "Gaussian measures" that there is a unique (up to equivalence $\mu$-almost everywhere) linear functional $\psi : X \to \mathbb{R}$ with $\phi = \psi$ on the Cameron-Martin space of $\mu$. But I do not see how to prove whether the equality would hold $\mu$-almost everywhere.