About the uniform approximation on the all real axis of continuous distribution functions

摘要

The theorem of V.I. Zubov about the possibility of uniform approximation on the all real axis for an arbitrary continuous distribution function with using approaching aggregates built on the basis of the one fixed continuous distribution function is developed in a number of ways. A certain type of approaching aggregates is shown, the estimations for approximation error are given in terms of moduli of continuity.