The uniform law of large numbers for the Kaplan-Meier integral process

Let U-n(f) = integral f d((F) over cap (n) - (F) over cap) be the function-indexed Kaplan-Meier integral process constructed from the random censorship model. We study a uniform version of the law of large number's of Glivenko-Cantelli type for {U-n} under the bracketing entropy condition. The main result is that the almost sure convergence and convergence in the mean of the process U-n holds uniformly in F. In proving the result we shall employ the bracketing method which is used in the proof of the uniform law of large numbers for the complete data of the independent and identically distributed model.