Construction and Characterisation of Stationary and Mass-Stationary Random Measures on ${\mathbb R}^d$

Mass-stationarity means that the origin is at a typical location in the mass of a random measure. It is an intrinsic characterization of Palm versions with respect to stationary random measures. Stationarity is the special case when the random measure is Lebesgue measure. The paper presents constructions of stationary and mass-stationary versions through change of measure and change of origin. Further, the paper considers characterizations of mass-stationarity by distributional invariance under preserving shifts against stationary independent backgrounds.