Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this chapter
Cite this chapter
van der Vaart, A.W., Wellner, J.A. (1996). Glivenko-Cantelli Theorems. In: Weak Convergence and Empirical Processes. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2545-2_16
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2545-2_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-2547-6
Online ISBN: 978-1-4757-2545-2
eBook Packages: Springer Book Archive