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An Abstract Law of Large Numbers

Al-Najjar, Nabil I. and Pomatto, Luciano (2020) An Abstract Law of Large Numbers. Sankhya A - The Indian Journal of Statistics, 82 (1). pp. 1-12. ISSN 0976-836X. doi:10.1007/s13171-018-00162-z.

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We study independent random variables (Z_i)_(i∈I) aggregated by integrating with respect to a nonatomic and finitely additive probability ν over the index set I. We analyze the behavior of the resulting random average ∫_IZ_idν(i). We establish that any ν that guarantees the measurability of ∫_IZ_idν(i) satisfies the following law of large numbers: for any collection (Zi)_(i∈I) of uniformly bounded and independent random variables, almost surely the realized average ∫_IZ_idν(i) equals the average expectation ∫_IE[Z_i]dν(i).

Item Type:Article
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Pomatto, Luciano0000-0002-4331-8436
Additional Information:© 2019 Indian Statistical Institute. Paper received: 25 February 2018; First Online: 17 January 2019.
Subject Keywords:Finitely additive probabilities; Measure theory; Measurability
Issue or Number:1
Classification Code:AMS (2000) subject classification: Primary 28A25; Secondary 60F15
Record Number:CaltechAUTHORS:20190404-160929922
Persistent URL:
Official Citation:Al-Najjar, N.I. & Pomatto, L. Sankhya A (2020) 82: 1.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94480
Deposited By: Tony Diaz
Deposited On:04 Apr 2019 23:20
Last Modified:16 Nov 2021 17:05

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