Metric results for dyadic approximation on the middle-third Cantor set

Xin-Rong Dai, Bing Li, Bo Wang +1

Let $C$ be the middle-third Cantor set and $\hat{I}¼$ be the Cantor-Lebesgue measure on $C$. A conjecture of Velani states that $\hat{I}¼(W_2(\ddot{I}„))=0$ if $\ddot{I}„>1$ and $\hat{I}¼(W_2(\ddot{I}„))=1$ if $0<τ\leq…