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We prove a martingale triangular array generalization of theChow-Birnbaum-Marshall's inequality. The result is used to derive a strong lawof large numbers for martingale triangular arrays whose rows are asymptoticallystable in a certain sense. To illustrate, we derive a simple proof, based onmartingale arguments, of the consistency of kernel regression with dependentdata. Another application can be found in \cite{atchadeetfort08} where the newinequality is used to prove a strong law of large numbers for adaptive MarkovChain Monte Carlo methods.

A strong law of large numbers for martingale arrays