Spaces of Bounded Measurable Functions Invariant under a Group Action

Abstract

In this paper, we characterize spaces of L∞-functions on a compact Hausdorff space that are invariant under a transitive and continuous group action. This work is analogous to established results concerning invariant spaces of continuous and measurable functions on a compact Hausdorff space. The case for L∞-functions cannot be proved in the same way when endowed with the norm-topology, but a similar argument can be used when the space of L∞-functions is given the weak*-topology, as we show in this paper.