This paper has been withdrawn Any real number $x$ in the unit interval can be expressed as a continued fraction $x=[n_1,...,n_{ _N},...]$. Subsets of zero measure are obtained by imposing simple conditions on the $n_{ _N}$. By imposing $n_{ _N}\le m \forall N\in \zN$, Jarnik defined the corresponding sets $E_m$ and gave a first estimate of $d_H(E_m)$, $d_H$ the Hausdorff dimension. Subsequent authors improved these estimates. In this paper we deal with $d_H(E_m)$ and $d_H(F_m)$, $F_m$ being the set of real numbers for which ${ \sum_{ i=1}^N n_i\over N}\le m$.
Categories: math.NT