Open Access
June, 1980 Log Log Laws for Empirical Measures
J. Kuelbs, R. M. Dudley
Ann. Probab. 8(3): 405-418 (June, 1980). DOI: 10.1214/aop/1176994716


Let $(X, \mathscr{A}, P)$ be a probability space and $\mathscr{C}$ a collection of measurable sets. Suppose $\mathscr{C}$ is a Donsker class, i.e., the central limit theorem for empirical measures holds uniformly on $\mathscr{C}$, in a suitable sense. Suppose also that suitable ($P\varepsilon$-Suslin) measurability conditions hold. Then we show that the $\log\log$ law for empirical measures, in the Strassen-Finkelstein form, holds uniformly on $\mathscr{C}$.


Download Citation

J. Kuelbs. R. M. Dudley. "Log Log Laws for Empirical Measures." Ann. Probab. 8 (3) 405 - 418, June, 1980.


Published: June, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0442.60031
MathSciNet: MR573282
Digital Object Identifier: 10.1214/aop/1176994716

Primary: 60F15
Secondary: 28A05 , 60F05

Keywords: Donsker class , empirical measures , Log log law

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 3 • June, 1980
Back to Top