1 results
Glivenko–Cantelli theorems for classes of convex sets
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- Journal:
- Advances in Applied Probability / Volume 11 / Issue 4 / December 1979
- Published online by Cambridge University Press:
- 01 July 2016, pp. 820-833
- Print publication:
- December 1979
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- Article
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Let
denote the empirical distribution obtained from a sequence of i.i.d. 
-valued random vectors with common distribution P. If 
is a class of Borel subsets of then we say that it forms a Glivenko–Cantelli class for P if
In this paper we describe a simple technique for identifying such classes, based on the idea of uniformity classes for setwise convergence. Classes for which the method proves successful include the closed half-spaces, closed balls, and the class of all convex subsets of .
denote the empirical distribution obtained from a sequence of i.i.d. 
-valued random vectors with common distribution 
is a class of Borel subsets of 
