  A set $E$ in a Banach space $X$ is compactivorous if for every compact set
$K$ in $X$ there is a nonempty, (relatively) open subset of $K$ which can be
translated into $E$. In a separable Banach space, this is a sufficient
condition which guarantees the Haar nonnegligibility of Borel subsets. We give
some characterisations of this property in both separable and nonseparable
Banach spaces and prove an extension of the main theorem to countable products
of locally compact Polish groups.
