Random measures

The present work is one of the main contributions to the fundamental, foundational work of the Jena school of probability in the sixtieth. Spiritus rector of this school was Johannes Kerstan who stimulated Klaus Matthes and Joseph Mecke. Their joint work culminated in the comprehensive monography 'Infinitely Divisible Point Processes' (1978, german edition 1974, russian edition 1982). It was completely written by Matthes, who included many results of Kerstan and Mecke. The great impact, the continued fertility and profound depth of their ideas from this period has now become manifest several decades later. In this context one should also mention the monography 'Stochastic Geometry and its Applications' written together with Dietrich Stoyan and Wilfrid Kendall (English edition 1995). This work contains several results not only of Joseph Mecke but also of D. G. Kendall. The habilitation work of Joseph Mecke, published and translated here for the first time together with a short unpublished note, is an early document of the theory of random measures which presents the complicated material in an accessible and elegant form. Even today, after forty years development of the subject, it can serve as an ideal textbook for advanced seminars in mathematics and thereby stimulate future research.