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Let $M([0,1])$ be the set of finite signed measures on $[0,1]$ (with the topology generated by the sets $\left\{ \mu \in M([0,1]) : \left| \int f(x) \mu(dx)- a\right| \leq \delta\right\}$ for all $\...

Below we use Bochner measurability and Bochner integral. Let $(Y, d)$ be a separable metric space, $\mathcal B$ Borel $\sigma$-algebra of $Y$, $\nu$ a $\sigma$-finite Borel measure on $Y$, $(Y, \...