Multifunctions on abstract measurable spaces and application to stochastic decision theory |
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Authors: | C J Himmelberg F S Van Vleck |
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Institution: | (1) Lawrence, Kansas |
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Abstract: | 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.
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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Keywords: | |
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