Sampling discretization error of integral norms for function classes with small smoothness

We consider infinitely dimensional classes of functions and instead the relative error setting, which was used in previous papers on integral norm discretization, we absolute setting. demonstrate how known results from two areas research – supervised learning theory numerical integration can be sampling discretization square different function classes. prove a general result, shows that sequence entropy numbers class uniform dominates, certain sense, errors this class. Then use result for establishing new bounds multivariate with mixed smoothness.