  We introduce canonical measures on a locally finite simplicial complex $K$
and study their asymptotic behavior under infinitely many barycentric
subdivisions. We also compute the face polynomial of the asymptotic link and
dual block of a simplex in the $d^{th}$ barycentric subdivision $Sd^d(K)$ of
$K$, $d\gg0$. It is almost everywhere constant. When $K$ is finite, we study
the limit face polynomial of $Sd^d(K)$ after F.Brenti-V.Welker and
E.Delucchi-A.Pixton-L.Sabalka.
