We provide some new Caratheodory-type selection theorems, i.e., selections for correspondences of two variables which are continuous with respect to one variable and measurable with respect to the other. These results generalize simultaneously Michael's continuous selection theorem for lower-semicontinuous correspondences as well as a Caratheodory-type selection theorem of Fryszkowski . Random fixed point theorems (which generalize ordinary fixed point theorems, e.g., Browder's ) follow as easy corollaries of our results.
Bibliographical noteFunding Information:
by an NSF grant
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