Let $X$ be locally Hausdorff space and let $M$ be the space of all complex Radon measure on $X$.
For a bounded Borel measurable function $\psi$ and $\mu\in M$, we define $$ \left(\mu\lfloor \psi\right)(E)=\int_E\psi(\xi)\mu(d\xi).$$
I need to proof that $\mu\lfloor \psi \in M$.
I have tried to prove the $\sigma-$additivity but I have not been able. And I don't know how proof that is Radon.