| 2 (2007) | |||||||||||||||
Abstract | |||||||||||||||
| Open Problem No. 12.2 of [8] asks: \Are the properties of uniform convergence of empirical means, and learnability preserved when the family of probability measures is replaced by its closure?" In this note, the question is answered in the armative. Further, it is shown that these properties are not preserved in general if the family of probability measures is replaced by its convex closure. An open question is posed as to whether it is possible to replace the family of probability measures by its convex closure in case the family is compact. Key Words: PAC learning, uniform convergence of empirical means, closure properties Running Head: Closure Properties All the work reported here was carried while the rst author was employed at CAIR, and the second and third authors visited CAIR, at separate points in time. B. Hammer is deeply indebted to the rst author for his warm hospitality during her visit to Bangalore. 1 | |||||||||||||||
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