  We prove that SU(N) bosonic Yang-Mills matrix integrals are convergent for
dimension (number of matrices) $D\ge D_c$. It is already known that $D_c=5$ for
N=2; we prove that $D_c=4$ for N=3 and that $D_c=3$ for $N\ge 4$. These results
are consistent with the numerical evaluations of the integrals by Krauth and
Staudacher.
