Uniform large and moderate deviations for functional empirical processes

For {Xi}i >= 1 a sequence of i.i.d. random variables taking values in a Polish space [Sigma] with distribution [mu], we obtain large and moderate deviation principles for the processes {n-1 [Sigma][nt]i = 1 [delta]Xi; t >= 0}n >= 1 and {n-1/2 [Sigma][nt]i = 1 ([delta]Xi - [mu]); t >= 0}n >= 1, respectively. Given a class of bounded functions F on [Sigma], we then consider the above processes as taking values in the Banach space of bounded functionals over F and obtain the corresponding (uniform over F), large and moderate deviation principles. Among the corollaries considered are functional laws of the iterated logarithm.