A semigroup setting for distance measures in connexion with Poisson approximation (Q801384)

A classical theorem of probability theory due to Poisson says that binomial distributions converge to the Poisson distribution. The two most important and well-investigated metrics in connection with Poisson approximation are the total variation distance d and the cumulative distribution distance \(d_ 0\). It is the aim of the present paper to show that in connection with Poisson approximation, both metrics can in a natural way be seen within the same semigroup framework.