Note, if we let go of the notions of intersections and unions of sets of random variables, if the notations of union and intersection are considered as joint and, somewhat metaphorically, as between, then we may define the information between two random variables A and B as 
and so on for more than two random variables. We then need to be able to imagine the ``between'' process of two random variables, and be able to take its union and intersection with other random variables in a fashion that satisfies the set union and intersection algebra. Then the inequalities above become equalities, and the information correlation functions on n random variables become 
times the information between the n random variables. The algebra is straightforward. The previous section shows how this fairly seductive labeling may lead the worker astray. For the generalized information correlation functions mentioned at the end of the previous section, the interpretation here is the information between the named reduced densities.