Strong Law of Large Numbers for Random Sets in Banach spaces

2024/10/07 by Vladimir Kadets, Kadets, V., Olesia Zavarzina +1
Decision Sciences · #46B09 #46B26 #46G10 #47H04 #60F15 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.2410.04832

openalex publication_date 2024/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Strong Law of Large Numbers (SLLN) for random variables or random vectors with different mathematical expectations easily reduces by means of shifts to SLLN for random variables or random vectors whose mathematical expectations are equal to zero. The situation changes for random sets, where shifts cannot reduce sets of more than one point to the set \0\. We study effects that appear because of this difference.

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