Abstract
We present a sufficient and necessary condition for a function module space $X$ to have the approximate hyperplane series property (AHSP). As a consequence, we have that the space ${\mathcal{C}}_{0}(L,E)$ of bounded and continuous $E$-valued mappings defined on the locally compact Hausdorff space $L$ has AHSP if and only if $E$ has AHSP.
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