Let $G$ be a semi simple Lie group. I'm particularly interested in $SL(n,\mathbb{R})$. It is proved in

I. E. Segal and J. von Neumann, A theorem on unitary representations of semisimple Lie groups, Annals of Mathematics 52 (1950), 509–517.

that measurable unitary representations of $G$ are actually continuous. Is this also true for finite-dimensional non-unitary representations?