A new notion of expectation (or distance average) of random closed sets based on their distance function representation is introduced. A general concept of the distance function is exploited to define the expectation, which is the set whose distance function is closest to the expected distance function of the original (random) set. This distance average can be applied to average non-convex and non-connected random sets. We establish some basic properties and prove limit theorems for the empirical distance average of i.i.d. random sets.

Random convex sets and integral geometry (msc 52A22), Geometric probability and stochastic geometry (msc 60D05), Spatial processes (msc 62M30)
CWI
Department of Operations Research, Statistics, and System Theory [BS]

Baddeley, A.J, & Molchanov, I.S. (1995). Averaging of random sets based on their distance functions. Department of Operations Research, Statistics, and System Theory [BS]. CWI.