This is an informal outline of a systematic approach to the various facets of conditioning in point processes, which the author has developed formally in the last three chapters of the third edition of this book ”Random measures” (1983; Zbl 0544.60053). It discusses the close connections and dualities between such concepts as the Gibbs kernel, Palm distributions and conditional intensity kernels of first or higher order, the various ways in which these arise either through limit procedures or by decomposition of the compound Campbell measure, etc.
The author’s aim is to help the reader develop an intuitive understanding to these connections, taking as his point of departure the conditional distribution of a point processes \(\xi\) in a region B, given the configuration in the complement \(B^ c\). The article opens with a motivating reference to local energy functions as they appear in the theory of Gibbs systems and concludes with a reference to certain similarities between conditional intensity kernels and dual previsible projections.