In this chapter we prove two types of Glivenko-Cantelli theorems. The first theorem is the simplest and is based on entropy with bracketing. Its proof relies on finite approximation and the law of large numbers for real variables. The second theorem uses random L 1-entropy numbers and is proved through symmetrization followed by a maximal inequality.
KeywordsConditional Expectation Empirical Process Envelope Function Measurable Cover Maximal Inequality
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