Spaces of Bounded Measurable Functions Invariant under a Group Action

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