Information contained in design points of experiments with correlated observations

A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points . The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this information is zero. Explicit expressions are obtained for the amount of information coming from a selected subset of a given design. Relations to some algorithms for optimum design of experiments in case of correlated observations are indicated.