Sums Of Cantor Sets From Lüroth Expansions

Let x ? (0,1] and the Liiroth expansion of x be defined as where ?n (x)?2 for all n?1. In this dissertation,we study the sum of Cantor sets from Liiroth expansion, with giving particular attention to the question of when the sum of L(N) form an interval. A analogous question arising from continued fraction expansions, another similar iterated function system, was first settled by Hall[21] in 1947. The main tool of our study is a fundamental theorem of Astels[1] about when the sum of Cantor sets is an interval.