Abstract
Based on an extension of Aumann’s measurable selection theorem due to Leese, it is shown that each fixed point theorem for F ( ω , ⋅ ) F(\omega , \cdot ) produces a random fixed point theorem for F F provided the σ \sigma -algebra Σ \Sigma for Ω \Omega is a Suslin family and F F has a measurable graph (in particular, when F F is random continuous with closed values and X X is a separable metric space). As applications and illustrations, some random fixed points in the literature are obtained or extended.
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