Convergence of subsets

The notion of convergence in the "Hausdorff metric" is used implicitly throughout this paper. However, since the concept will not be used in its full generality, the following notation is introduced for the special case of interest here.

Let , , be a sequence of subsets of , and let . The notation

means that

Recall that, if is compact for every , then so is . If, in addition, each is nonempty, then so is .