Association rules mining is a problem that has given rise to a rich literature, especially in classic binary bidimensional data. In particular, the representation of the set of rules without loss of information is well understood. This is not the case in multidimensional binary data. In this paper, we show that the knowledge of the closed $n$-sets of a multidimensional Boolean tensor is enough to allow for the derivation of the confidence of every multidimensional association rule. This generalises well-known results in the bidimensional case. We also provide experimental comparisons between the numbers of closed $n$-sets and frequent associations.