Martin-Löf random generalized Poisson processes

Martin-Löf randomness was originally defined and studied in the context of the Cantor space 2ω . In [1] probability theoretic random closed sets (RACS) are used as the foundation for the study of Martin-Löf randomness in spaces of closed sets. Here we focus on the space of closed subsets of R and a particular family of measures on this space, the generalized Poisson processes. This gives a novel class of Martin-Löf random closed subsets of R. We begin studying these Martin-Löf random closed sets, proving in part that the elements of these sets are themselves Martin-Löf random.