Summary
The main results are some very general theorems about measurable multifunctions on abstract measurable spaces with compact values in a separable metric space. It is shown that measurability is equivalent to the existence of a pointwise dense countable family of measurable selectors, and that the intersection of two compact-valued measurable multifunctions is measurable. These results are used to obtain a Filippov type implicit function theorem, and a general theorem concerning the measurability of y(t)=min f({t} × Γ(t)) when f is a real valued function and Γ a compact valued multifunction. An application to stochastic decision theory is given generalizing a result of Benes.
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The research in this paper was partially supported by University of Kansas General Research Fund Grants 3918-5038 and 3199-5038.
Entrata in Redazione il 20 dicembre 1972.
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Himmelberg, C.J., Van Vleck, F.S. Multifunctions on abstract measurable spaces and application to stochastic decision theory. Annali di Matematica 101, 229–236 (1974). https://doi.org/10.1007/BF02417106
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DOI: https://doi.org/10.1007/BF02417106