Abstract
The following old problem is solved. Given an e> 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(e) of measure larger than 1-e 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- e) estimate of partial uniform moduli of continuity and write out this estimate of the uniform partial moduli of continuity.
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