A NEW APPROACH TO COVERING

For finite coverings in euclidean d-space E(d) we introduce a parametr ic density function. Here the parameter controls the influence of the boundary of the covered region to the density. This definition gives a new approach to covering which is similar to the approach for packing in [BHW1], [BHW2]. In this way we obtain a unified theory for finite and infinite covering and generalize similar results, which were devel oped by various authors since 1950 for d = 2, to all dimensions.