  We aim to link random fields and marked point processes and therefore
introduce a new class of stochastic processes which are defined on a random set
in R^d. Unlike for random fields, the mark covariance function of a marked
random set is in general not positive definite. This implies that in many
situations the use of simple geostatistical methods appears to be questionable.
Surprisingly, for a special class of processes based on Gaussian random fields,
we do have positive definiteness for the corresponding mark covariance function
and mark correlation function.
