Sampling and interpolation of cumulative distribution functions of Cantor sets in [0, 1]

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