Abstract
Let be a Lebesgue measurable subset of a -dimensional cube (), let , where , and let be the least deviation of , in the metric of , from the rational functions of degree . If , then, for , has a local differential of order in the -metric at each point , except perhaps points of some set of metric dimension (this inequality is sharp). In addition, has a global differential of order in the metric of for any .Bibliography: 15 titles.
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