Results on Central Limit Theorems for Empirical Process

We cretically examine and formulate some new results in Emperical process on central limit theorem we mainly put emphassion comparison theorem for Rademacher averages which is at the basis of the results with applications, in particular, to Kolmogorov’s law of the interated logarithm and Prokhorov’s law of large numbers for empirical processes. The main objective is to develop, with applications, some devices in these directions. We show how the Gaussian randomization can efficiantly be replaced to allow the investigation on non-equidistributed situation and how it is possible to make use of a pregaussian structure even if not explicatly given to described empitical processes on clauss of functions.