A fixed point theorem for measurable selection valued correspondences induced by upper Caratheodory correspondences

Jing Fu and Frank Page

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We show that any measurable selection valued correspondence induced by the composition of an m-tuple of real-valued Caratheodory functions with an upper Caratheodory (uC) correspondence has fixed points if the underlying uC correspondence in the composition contains a continuum valued uC sub-correspondence. Moreover, this composition of the m-tuple of real-valued Caratheodory functions with the continuum valued uC sub-correspondence induces a measurable selection valued sub-correspondence that is weak star upper semicontinuous.

Keywords: m-tuples of Caratheodory functions; upper Caratheodory correspondences; continuum valued upper Caratheodory sub-correspondences; approximate Caratheodory selections; fixed points of nonconvex; measurable selection valued correspondences induced by the composition of an m-tuple of Caratheodory functions with a continuum valued upper Caratheodory sub-correspondence (search for similar items in EconPapers)
JEL-codes: C70 (search for similar items in EconPapers)
Pages: 10 pages
Date: 2022-03-25
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