A Mecke-type characterization of the Dirichlet-Ferguson measure

TL;DR

This paper characterizes the Dirichlet-Ferguson measure on any finite diffuse measure space, drawing an analogy with the Mecke identity for Poisson processes, thus extending understanding of this measure.

Contribution

It provides a novel Mecke-type characterization of the Dirichlet-Ferguson measure applicable to arbitrary finite diffuse measure spaces.

Findings

Established a Mecke-type identity for the Dirichlet-Ferguson measure.

Extended the characterization of the Dirichlet-Ferguson measure to general finite diffuse spaces.

Provided an interpretative framework linking the measure to Poisson process identities.

Abstract

We prove a characterization of the Dirichlet-Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes.