  We study dynamical systems $(X,G,m)$ with a compact metric space $X$ and a
locally compact, $\sigma$-compact, abelian group $G$. We show that such a
system has discrete spectrum if and only if a certain space average over the
metric is a Bohr almost periodic function. In this way, this average over the
metric plays for general dynamical systems a similar role as the
autocorrelation measure plays in the study of aperiodic order for special
dynamical systems based on point sets.

Dynamical Systems