  The Fock transform recently introduced by the authors in a previous paper is
applied to investigate convergence of generalized functional sequences of a
discrete-time normal martingale $M$. A necessary and sufficient condition in
terms of the Fock transform is obtained for such a sequence to be strong
convergent. A type of generalized martingales associated with $M$ are
introduced and their convergence theorems are established. Some applications
are also shown.
