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Remarks on Measurable Selections
R. B. Darst
The Annals of Statistics
Vol. 2, No. 4 (Jul., 1974), pp. 845-847
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2958424
Page Count: 3
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Many authors have studied the problem of obtaining an optimal plan for a dynamic programming problem or a stochastic game. In several of these works a maximal selection theorem of Dubins and Savage for u.s.c. (upper-semi-continuous) maps has played a key role. Our purpose is to relax the requirements that the maps be u.s.c. and still obtain maximal or at least nearly maximal selections.
The Annals of Statistics © 1974 Institute of Mathematical Statistics