Talk:Random compact set

This article, while having some good information, needs some work. I will probably try my hand at this over the next couple of months.

Definition includes a proposition without acknowledging it ?
"Put another way, a random compact set is a measurable function $$K \colon \Omega \to 2^{M}$$ such that $$K(\omega)$$ is almost surely compact and


 * $$\omega \mapsto \inf_{b \in K(\omega)} d(x, b)$$

is a measurable function for every $$x \in M$$."

This is not obvious. And the phrase "put another way" might be obscuring the true logical relationship between the definition proper and this new statement.. Does the statement about the distance function to a random set being measurable follow from the measurability of K? Is it equivalent to it? In the latter case, shouldn't we remove the stipulation that K is a measurable function from the above formulation?

50.255.2.98 (talk) 22:12, 13 March 2016 (UTC)