  We introduce the "relative diffuseness" assumption to characterize the
differences between payoff-relevant and strategy-relevant diffuseness of
information. Based on this assumption, the existence of pure strategy
equilibria in games with incomplete information and general action spaces can
be obtained. Moreover, we introduce a new notion of "undistinguishable
purification" which strengthens the standard purification concept, and its
existence follows from the relative diffuseness assumption.
