Closure of Random samples

2010/08/27 by Reza Hosseini, Hosseini, Reza
Decision Sciences · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1008.4818

arxiv created 2010/08/27 · openalex publication_date 2010/08/27 · arxiv updated 2010/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that the closure of a random sample for a k-dimensional random vector is almost surely a deterministic set of all heavy points of the distribution. A heavy point is defined to be a point for which all its neighborhoods have positive probability.

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