Summary.We establish large deviation principles for the stationary and the individual empirical fields of Poisson, and certain interacting, random fields of marked point particles in IR~. The underlying topologies are induced by a class of not necessarily bounded local functions, and thus finer than the usual weak topologies. Our methods yield further that the limiting behaviour of conditional Poisson distributions, as well as certain distributions of Gibbsian type, is governed by the maximum entropy principle. We also discuss various applications and examples.

Dedicated to Klaus Krickeberg on the occasion of his 50th birthday Summary. We investigate the ergodic properties of spatial processes, i.e. stochastic processes with an index set of bounded Borel subsets in IR v, and prove mean and individual ergodic theorems for them. As important consequences we get a generalization of McMillan's theorem due to Fritz [4]; the existence of specific energy for a large class of interactions in the case of marked point processes in IR v and the existence of the specific Minkowski QuermaBintegrats for Boolean models in IR ~ with convex, compact grains.

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