World Flash on Basic Research

An incomplete bibliography (or, more generally, an incomplete Information Production Process (IPP)) can be considered as a sample from a complete one. Sampling can be done in the sources or in the items. The simplest sampling technique is the systematic one where every kth source or kth item is taken (alternatively: deleted) (kÎû). In this paper we give a definition of systematic sampling in items and sources in the framework of an IPP in which we have continuous variables. We prove the theorem that in such IPPs we have a Lotkaian size-frequency function (i.e. a decreasing power function) if and only if systematic sampling in sources is the same as systematic sampling in items. In this proof we use the well-known characterization of power functions as scale-free functions.