Random approximation of Sobolev embeddings (Q1179456)

A wealth of far reaching definitions and heavy theory, nicely compressed into short, yet mighty, symbols --- familiar to concepts of information- based complexity and approximation theory --- serve to allow a definition of Monte-Carlo methods as a probability on a space of methods based on linear operators together with appropriately derived general function spaces. They provide the tools for the intended theorems concerning estimates, mostly sharp ones, for the Monte-Carlo approximation. By the resulting theorems the right order of magnitude of the considered approximations is obtained. They give estimations for standard approximation numbers and their averages.