On the modified Palm version

The interpretation of the 'standard' Palm version of a stationary random measure xi is that it behaves like xi conditioned on containing the origin in its mass. The interpretation of the 'modified' Palm version is that it behaves like xi seen from a typical location in its mass. In this paper we shall focus on the modified Palm version, comparing it with the standard version in the transparent case of mixed biased coin tosses, and then establishing a limit theorem that motivates the above interpretation in the case of random measures on locally compact second countable Abelian groups possessing Folner averaging sets.