If $(\Omega ,\Sigma )$ is a measurable space and $X$ a Banach space, we provide sufficient conditions on $\Sigma$ and $X$ in order to guarantee that $\mathrm{b}vca(\Sigma ,X)$, the Banach space of all $X$-valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of $c_0$ if and only if $X$ does.

Utilizing elementary properties of convergence of numerical sequences we prove Nikodym, Banach, Orlicz-Pettis type theorems