On liftings and the regularization of stochastic processes (Q1092513)

We show that not all liftings are suitable tools for the regularization of stochastic processes. Under continuum hypothesis, we construct a Glivenko-Cantelli class Z on [0,1] and a lifting \(\rho\) of \(L^{\infty}\) such that \(\rho\) Z is not a Glivenko-Cantelli class. This strongly contrasts with the fact, shown earlier by the author, that some special liftings have excellent regularization properties.