On the conditions when the cylindrical measure on cojugate Banach space may be extended to Radon measure

In an arbitrary Banach space $E$ we define the local convex topologies $t_N(E)\ge t_S(E)$. Let $\lambda$ be an arbitrary cylindrical probability on $E'$. We prove that continuity of $\lambda$ with respect to $t_N(E)$ ($t_S(E)$) is a necessary (sufficient) condition for $\lambda$ may be extended to a Radon measure on $E'$. If $E$ is Hilbertian then the topologies $t_N(E)$ and $t_S(E)$ are identical to $J$-topology introduced by V. V. Sazonov. Conversely, if $t_N(E)=t_S(E)$ then $E$ is Hilbertian.