by:L. Dubins, Ashok P. Maitra, R. Purves, William D. Sudderth
The optimal return function for a Borel measurable gambling problem with a bounded utility function was shown by Strauch (1967) to be universally measurable when the problem is leavable in the sense that the gambler may terminate play at any time. The same is shown here for the more general class of nonleavable problems. Research supported by National Science Foundation Grant DMS-8801085.
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