About the mutual (conditional) information

We give a necessary, sufficient, and easily verifiable criterion for the conditional probability distribution P/sub Z|XY/ (where X, Y and Z are arbitrary random variables), such that I(X; Y)/spl ges/I(X; Y|Z) holds for any distribution P/sub XY/. Furthermore, the result is generalized to the case where Z is specified by a conditional probability distribution depending on more than two random variables.