On the Existence and Convergence of Probability Measures on Continuous Semi-Lattices.

Abstract

This paper studies probability measures on continuous lattices and, more generally, continuous semi-lattices. It characterizes probability measures by distribution functions, it characterizes weak convergence of probability measures by pointwise convergence of distribution functions and it provides a Levy-Khinchin representation of all infinitely divisible distributions. By applying the general results to special cases this paper extends some well-known results for random closed sets in locally compact second countable Hausdorff spaces to non-Hausdorff spaces. It also provides some new results for random compact sets and random compact convex sets in Euclidean spaces.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1986
Accession Number
ADA179267

Entities

People

  • Tommy Norberg

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Continuity
  • Convergence
  • Convex Sets
  • Distribution Functions
  • Filters
  • Functions (Mathematics)
  • Mathematics
  • North Carolina
  • Probability
  • Random Variables
  • Sequences
  • Set Theory
  • Stochastic Processes
  • Theorems
  • Topology
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space