  We obtain some maximal probability and moment inequalities for
multidimensionally indexed demimartingales. Although the class of
single-indexed demimartingales has been studied extensively, no significant
amount of work has been done for the corresponding multiindexed class of random
variables. This work aims to fill in this gap in the literature by extending
well-known inequalities and asymptotic results to this more general class of
random variables.
