@article{Gu_Jiang_Xi_Zhao_2021, title={Multiplication on uniform λ-Cantor sets}, volume={46}, url={https://afm.journal.fi/article/view/110571}, abstractNote={<p> </p> <pre>Let \(C\) be the middle-third Cantor set. Define \(C*C=\{x*y\colon x,y\in C\}\), where \(*=+,-,\cdot,\div\) (when \(*=\div\), we assume \(y eq0\)). Steinhaus [17] proved in 1917 that</pre> <pre>\(C-C=[-1,1]\), \(C+C=[0,2]\).</pre> <pre>In 2019, Athreya, Reznick and Tyson [1] proved that</pre> <pre>\(C\div C=\bigcup_{n=-\infty}^{\infty}\left[ 3^{-n}\dfrac{2}{3},3^{-n}\dfrac {3}{2}\right] \cup \{0\}\).</pre> <pre>In this paper, we give a description of the topological structure and Lebesgue measure of \(C\cdot C\). We indeed obtain corresponding results on the uniform \(\lambda\)-Cantor sets.</pre>}, number={2}, journal={Annales Fennici Mathematici}, author={Gu, Jiangwen and Jiang, Kan and Xi, Lifeng and Zhao, Bing}, year={2021}, month={Aug.}, pages={703–711} }