On Deterministic and Random Fixed Points

Abstract

Abstract.Based on an extension of Aumann's measurable selection theorem due to Leese, it is shown that each fixed point theorem for F{w, •) produces a random fixed point theorem for F provided the rj-algebra X for Sl is a Suslin family and F has a measurable graph (in particular, when F is random continuous with closed values and A' is a separable metric space). As applications and illustrations, some random fixed points in the literature are obtained or extended.