Log Log Laws for Empirical Measures
Kuelbs, J. ; Dudley, R. M.
Ann. Probab., Tome 8 (1980) no. 6, p. 405-418 / Harvested from Project Euclid
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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 $\mathscr{C}$.
Publié le : 1980-06-14
Classification:  Log log law,  empirical measures,  Donsker class,  60F15,  60F05,  28A05 
@article{1176994716,
     author = {Kuelbs, J. and Dudley, R. M.},
     title = {Log Log Laws for Empirical Measures},
     journal = {Ann. Probab.},
     volume = {8},
     number = {6},
     year = {1980},
     pages = { 405-418},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176994716}
}

Kuelbs, J.; Dudley, R. M. Log Log Laws for Empirical Measures. Ann. Probab., Tome 8 (1980) no. 6, pp.  405-418. http://gdmltest.u-ga.fr/item/1176994716/