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Cantor sets are constructed from iteratively removing sections of intervals.This process yields a cumulative distribution function (CDF), constructed fromthe invariant measure associated with their iterated function systems. Underappropriate assumptions, we identify sampling schemes of such CDFs, meaningthat the underlying Cantor set can be reconstructed from sufficiently manysamples of its CDF. To this end, we prove that two Cantor sets havealmost-nowhere (with respect to their respective invariant measures)intersection.

Almost-nowhere intersection of Cantor sets, and sufficient sampling of their cumulative distribution functions