The Structure Of Sums Of Cantor Sets

Abstract:This paper is concerned with the structure of arithmetic sums of Cantor sets,such as topological structure, measure structure and fractal structure,which has been studied during recent 40 years.There are theorems on the structure of sums of Cλs, homogeneous Cantor sets,Cantor sets with constant ratios of dissection at each step,and so on.A main tool for these theorems is the duality between the set of subsums of certain series and Cantor sets.for it easily describes the local feature of a set.Another interesting thing is to examine various criteria under which C1+C2+…+Ck contains an interval,and thickness is a useful tool for this.Fractal structure of the sums of Cantor sets is also introduced.