VII: 16, 155-171, LNM 321 (1973)
MEYER, Paul-André;
TRAKI, Mohammed
Réduites et jeux de hasard (
Potential theory)
This paper arose from an attempt (by the second author) to rewrite the results of Dubins-Savage
How to Gamble if you Must in the language of standard (countably additive) measure theory, using the methods of descriptive set theory (analytic sets, section theorems, etc). The attempt is successful, since all general theorems can be proved in this set-up. More recent results in the same line, due to Strauch and Sudderth, are extended too. An appendix includes useful comments by Mokobodzki on the case of a gambling house consisting of a single kernel (discrete potential theory)
Comment: This material is reworked in Dellacherie-Meyer,
Probabilités et Potentiel, Vol. C, Chapter X
Keywords: Balayage,
Gambling house,
Réduite,
Optimal strategyNature: Original
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