The Correction Theorem for Anisotropic Spaces

The following old problem is solved. Given an ε> 0, a function f:[0,1]n→ ℝ, and the partial moduli of continuity of this function evaluated in a symmetric space X, find a set I(ε) of measure larger than 1-ε such that the partial uniform moduli of continuity of f determined for the points of this set admit an unimprovable (with respect to all restrictions to sets of measure larger than 1- ε) estimate of partial uniform moduli of continuity and write out this estimate of the uniform partial moduli of continuity.