The bayesian formulation of incomplete information - The non-compact case

In a game with incomplete information, a player may have beliefs about nature, about the other players' beliefs about nature, and so on, in an infinite hierarchy. We generalize a construction of Mertens & Zamir and show, that if nature is any Hausdorff space, and beliefs are regular Borel probability measures, then the space of all such infinite hierarchies of the players is a product of nature and the types of every player, where a type of a player is a belief about nature and the other players' types.