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

Asymptotic mean stationarity and absolute continuity of point process distributions