Dispersion Measures and Multidistances on $\mathbb {R}^k$

Abstract

After introducing a definition of dispersion measure on the Euclidean space $\mathbb {R}^k$, we deal with the connection between these measures and the so called multidistances. In this way, we show that thr standard deviation is a relevant example of multidistance and, on the other hand, several significant families of multidistances are, at the same time, dispersion measures. Sufficient conditions for a multidistance to be a dispersion measure are also established.