On the Existence and Convergence of Probability Measures on Continuous Semi-Lattices.
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
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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.
- Statistics and Probability