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Some Measurability Results for Extrema of Random Functions Over Random Sets

Maxwell B. Stinchcombe and Halbert White
The Review of Economic Studies
Vol. 59, No. 3 (Jul., 1992), pp. 495-514
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/2297861
Page Count: 20
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Some Measurability Results for Extrema of Random Functions Over Random Sets
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Abstract

We consider the question, "Under what conditions is the extremum of a random function over a random set itself a random object?" The answer is relevant to problems in both game theory and econometrics, as we illustrate with examples. Our purpose here is to bring the powerful tools of the theory of analytic sets as developed by Dellacherie and Meyer (1978) to the wider attention of the economics profession and to distill Dellacherie and Meyer's work in such a way as to provide some readily accessible theoretical results that will permit relatively easy treatment of economically or econometrically relevant applications.

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