The law of large numbers is studied under a weakening of the axiomatic properties of a
probability measure. Averages do not generally converge to a point, but they are …

In this paper, we discuss a potential agenda for future work in the theory of random sets and
belief functions, touching upon a number of focal issues: the development of a fully-fledged …

Uncertainty is of paramount importance in artificial intelligence, applied science, and many
other areas of human endeavour. Whilst each and every one of us possesses some intuitive …

It is a celebrated result in the theory of random sets that, in a locally compact second
countable Hausdorff space, distributions of random closed sets are in one-to-one …

The study of random geometrical objects goes back to the famous Buffon needle problem.
Similar to the ideas of Geometric Probability, which can be traced back to the very origins of …

An integral representation theorem for outer continuous and inner regular belief measures
on compact topological spaces is elaborated under the condition that compact sets are …

A random set is a multivalued measurable function defined on a probability space. If this
multivalued function depends on the second argument (eg, time or space), then random …

The space 𝔽 F of closed sets (and also the space 𝕂 K of compact sets) is non-linear, so that
conventional concepts of expectations in linear spaces are not directly applicable for …

As the name suggests, a random set is an object with values being sets, so that the
corresponding record space is the space of subsets of a given carrier space. At this stage, a …

This paper discusses the definition of independence used in the proof of a law of large
numbers for upper expectations [Z. Chen, P. Wu, B. Li (2013). Int. J. Approx. Reasoning 54 …