  There have been, over the last 8 years, a number of far reaching extensions
of the famous original F. and M. Riesz's uniqueness theorem that states that if
a bounded analytic function in the unit disc of the complex plane $\Bbb C$ has
the same radial limit in a set of positive Lebesgue measure on its boundary,
then the function has to be constant. First Beurling [B], considering the case
of non-constant meromorphic functions mapping the unit disc on a Riemann
surface of finite spherical area, was able to prove that if such a function
showed an appropriate behavior in the neighborhood of the limit value where the
function maps a set on the boundary of the unit disc, then those sets have
logarithmic capacity zero. The author of the present note, in [V], was able to
weaken Beurling's condition on the limit value.
  Those results where quite restrictive in a two folded way, namely, they were
in dimension $n=2$ and the regularity requirements on the treated functions
were quite strong. Koskela in [K], was able to remove those two restrictions by
proving a uniqueness result for functions in $ACL^p(\Bbb B^n)$ for values of
$p$ in the interval $(1,n]$. Koskela also shows in his paper that his result is
sharp..
