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added the (hausdorff-dimension) tag
Martin Sleziak
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A set whose Hausdorff dimention gradually changes?

Can there be a set whose Hausdorff dimension gradually changes?

For instance, a set of real numbers contained in an interval, whose Hausdorff dimension is 0 at the beginning and 1 closer to the end, and changes without jumps?

Anixx
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