On some topological properties of countably additive cylindrical measures

Let $E$ be a Hausdorff locally convex space, $E'$ denotes the topological dual space of $E$. Let $\lambda$ he a cylindrical measure on $E'$. We prove that for a wide class of locally convex spaces $E$ the measure $\lambda$ is countably additive iff $\lambda$ is cylindrically concentrated on the paving of polars of origin's neighbourhood in $E$.