Compactivorous Sets in Separable Banach Spaces

Davide Ravasini

Published 2021-04-06Version 1

In a separable Banach space, the compactivorous property is a sufficient condition which guarantees the Haar nonnegligibility of Borel subsets. A set $E$ in a separable 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 $E$. We give some characterisations of this property and prove an extension of the main theorem to countable products of locally compact Polish groups.