A multivariate version of such a decomposition is presented in the paper for
a class of random fields generated by several commuting non-invertible
probability preserving transformations. In this representation summands of mixed
type appear which behave with respect to some group
of directions of the parameter space as reversed multiparameter martingale
differences (in the sense of one of
several known definitions) while they look as coboundaries relative to
the other directions. Applications to limit theorems will be published
elsewhere.
Keywords: random field, martingale difference, coboundary