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countably additive vector measure of bounded variation; Pettis integrable function space; copy of $c_{0}$; copy of $\ell _{\infty }$
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 $\mathop {\mathrm bvca}( \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.
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