  We consider anyonic excitations classified into equivalence classes labeled
by Hausdorff dimension, $h$ and introduce the concept of duality between such
classes, defined by $\tilde{h}=3-h$. In this way, we confirm that the filling
factors for which the Fractional Quantum Hall Effect (FQHE) were observed just
appears into these classes and the duality in case is between quasihole and
quaasiparticle excitations for these FQHE systems.Exchanges of dual pairs
$(\nu,\tilde{\nu})$, suggests conformal invariance.
