A note on dyadic approximation in Cantor's set

We consider the convergence theory for dyadic approximation in the middle-third Cantor set, , for approximation functions of the form (). In particular, we show that for values of beyond a certain threshold we have that almost no point in is dyadically -well approximable with respect to the natural probability measure on . This refines a previous result in this direction obtained by the first, third, and fourth named authors