I am almost certain that I read somewhere that the following is true, but I cannot seem to locate the reference. I would be most appreciative if someone could point me to a reference. The result was in one of the following forms.

Premise:Let $X$ be a Polish space. Let $S$ be the vector space of totally finite signed Borel measures on $X$. Let $T_N$ be the topology induced by the total variation norm on $S$. Let $T_{WC}$ be the topology of weak convergence of measures on $S$ (sometimes called the weak* topology).

Conclusion:Then the Borel $\sigma$-algebras generated by $T_N$ and $T_{WC}$ are the same.

Other form (which would imply the above):

Premise:Let $X$ be a measurable space with a countably generated $\sigma$-algebra. Let $S$ be the vector space of totally finite signed measures on $X$. Let $T_N$ be the topology induced by the total variation norm on $S$. Let $A$ be the $\sigma$-algebra on $S$ generated by maps of the form $\mu \mapsto \int_X f d\mu$ where $f\colon X \to \mathbb{R}$ varies over bounded measurable real-valued functions on $X$.

Conclusion:Then $A$ is equal to the Borel $\sigma$-algebras generated by $T_N$.