The sets of the form $C + mC$, where $m \in 2 (0; 1)$ and$C$ is the classic Cantor ternary set, are described.
@article{240,
title = {Linear combinations of the classic Cantor set},
journal = {Tatra Mountains Mathematical Publications},
volume = {55},
year = {2013},
doi = {10.2478/tatra.v56i0.240},
language = {EN},
url = {http://dml.mathdoc.fr/item/240}
}
Pawlowicz, Marta. Linear combinations of the classic Cantor set. Tatra Mountains Mathematical Publications, Tome 55 (2013) . doi : 10.2478/tatra.v56i0.240. http://gdmltest.u-ga.fr/item/240/