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