Hausdorff dimension of sets arising in Diophantine approximation

抄録

Let g(q) be a nonnegative function on the set of positive integers. We studied the Hausdorff dimension of a set
E_g={x∈[0, 1]: |x−\frac{p}{q}|<g(q)   for infinitely many \frac{p}{q}}.
We prove a generalization of a result of I. Borosh and A. S. Fraenkel.