  We prove a martingale triangular array generalization of the
Chow-Birnbaum-Marshall's inequality. The result is used to derive a strong law
of large numbers for martingale triangular arrays whose rows are asymptotically
stable in a certain sense. To illustrate, we derive a simple proof, based on
martingale arguments, of the consistency of kernel regression with dependent
data. Another application can be found in \cite{atchadeetfort08} where the new
inequality is used to prove a strong law of large numbers for adaptive Markov
Chain Monte Carlo methods.
