Annali di Matematica Pura ed Applicata

, Volume 101, Issue 1, pp 229–236 | Cite as

Multifunctions on abstract measurable spaces and application to stochastic decision theory

  • C. J. Himmelberg
  • F. S. Van Vleck


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.


Measurable Space Decision Theory Implicit Function Theorem General Theorem Countable Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1974

Authors and Affiliations

  • C. J. Himmelberg
    • 1
  • F. S. Van Vleck
    • 1
  1. 1.Lawrence

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