Randomizable point systems

This paper gives a survey of the theory of point-set randomizations with respect to a group. It is shown that only the so-calledk-lattices are randomizable with respect to the parallel translations and all motions of theR ⁿ space. It is shown how the randomizability problems are connected with questions of the theory of discrete Lie groups and regular point systems. The results are applied to the construction of stationary random line processes.