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 $\mu$ be the Cantor-Lebesgue measure on $C$. A conjecture of Velani states that $\mu (W_2(\tau ))=0$ if $\tau >1$ and $\mu (W_2(\tau ))=1$ if $0<\tau \le 1$, wh…