Same Gaps, Different Sets: A Survey on Complimentary sets and their Dimensions

Let a=\{a_n\} be a non-increasing sequence of positive real numbers adding up to $1$. Cutting out of the unit interval disjoint open gaps of lengths $a_1,a_2,\dots$, one for each term, leaves a compact set of Lebesgue measure zero, and since the gaps can be placed in infinitely many ways, there are