The Multiinformation Function As A Tool For Measuring Stochastic Dependence

. Given a collection of random variables [¸ i ] i2N where N is a finite nonempty set, the corresponding multiinformation function ascribes the relative entropy of the joint distribution of [¸ i ] i2A with respect to the product of distributions of individual random variables ¸ i for i 2 A to every subset A ae N . We argue it is a useful tool for problems concerning stochastic (conditional) dependence and independence (at least in discrete case). First, it makes possible to express the conditional mutual information between [¸ i ] i2A and [¸ i ] i2B given [¸ i ] i2C (for every disjoint A; B; C ae N) which can be considered as a good measure of conditional stochastic dependence. Second, one can introduce reasonable measures of dependence of level r among variables [¸ i ] i2A (where A ae N , 1 r ! card A) which are expressible by means of the multiinformation function. Third, it enables one to derive theoretical results on (nonexistence of an) axiomatic characterization of stochastic c..