Large deviations for products of empirical probability measures in the \(\tau\)-topology (Q1374850)

It is shown, that a large deviation principle for products of empirical measures, where the state space \(S\) of the underlying sequence of i.i.d. random variables is Polish and the set of probability measures on \(S\) respectively \(S\times S\) is endowed with the \(\tau\)-topology. An improved form of a large deviation principle for \(U\)-statistics and some conclusions from that are obtained as a particular application.