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Weak convergence of probability measures on hyperspaces with the upper Fell-topology

Dietmar Ferger

Abstract

Let E be a locally compact second countable Hausdorff space and F the pertaining family of all closed sets. We endow F respectively with the Fell-topology, the upper Fell topology or the upper Vietoris-topology and investigate weak convergence of probability measures on the corresponding hyperspaces with a focus on the upper Fell topology. The results can be transferred to distributional convergence of random closed sets in E with applications to the asymptotic behavior of measurable selection.

Weak convergence of probability measures on hyperspaces with the upper Fell-topology

Abstract

Let E be a locally compact second countable Hausdorff space and F the pertaining family of all closed sets. We endow F respectively with the Fell-topology, the upper Fell topology or the upper Vietoris-topology and investigate weak convergence of probability measures on the corresponding hyperspaces with a focus on the upper Fell topology. The results can be transferred to distributional convergence of random closed sets in E with applications to the asymptotic behavior of measurable selection.
Paper Structure (4 sections, 20 theorems, 58 equations)

This paper contains 4 sections, 20 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. Weak convergence of probability measures on the hyperspace $(\mathcal{F}, \tau_{uF})$
  3. Distributional convergence of random closed sets in $(\mathcal{F},\tau_{uF})$
  4. Appendix

Key Result

Proposition 1

The following two statements (i) and (ii) are equivalent:

Theorems & Definitions (38)

  • Proposition 1
  • Corollary 1
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Proposition 3
  • proof
  • Lemma 1
  • proof
  • ...and 28 more