A Generalization of the Monotonic and Boolean Independence of Algebras and Applications to Probability

抄録

We present a notion of bm-independence, which generalizes the boolean and monotonic independences. The generalization is defined for partially ordered index sets. For each independence there is an analogue of the classical central limit theorem. In the case of bm-independence this depends also on the index set. Examples of such partially ordered index sets are discrete lattices in symmetric positive cones.