  This paper relates - for point processes $\Phi$ on $\mathbb{R}$ - two types
of asymptotic mean stationarity (AMS) properties and several absolute
continuity results for the common probability measures emerging from point
process theory. It is proven that $\Phi$ is AMS under the time-shifts if and
only if it is AMS under the event-shifts. The consequences for the accompanying
two types of ergodic theorem are considered. Furthermore, the AMS properties
are equivalent or closely related to several absolute continuity results. Thus,
the class of AMS point processes is characterized in several ways. Many results
from stationary point process theory are generalized for AMS point processes.
To obtain these results, we first use Campbell's equation to rewrite the
well-known Palm relationship for general nonstationary point processes into
expressions which resemble results from stationary point process theory.
