A note on dyadic approximation in Cantor's set

This is the final version. Available on open access from Elsevier via the DOI in this recordWe consider the convergence theory for dyadic approximation in the middlethird Cantor set, K, for approximation functions of the form ψτ(n) = n−τ (τ ⩾ 0). In particular, we show that for values of τ beyond a certain threshold we have that almost no point in K is dyadically ψτ-well approximable with respect to the natural probability measure on K. This refines a previous result in this direction obtained by the first, third, and fourth named authors