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. https://resolver.caltech.edu/CaltechAUTHORS:20190404-160929922
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Abstract
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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| 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 | |||||||||
| DOI: | 10.1007/s13171-018-00162-z | |||||||||
| Record Number: | CaltechAUTHORS:20190404-160929922 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190404-160929922 | |||||||||
| Official Citation: | Al-Najjar, N.I. & Pomatto, L. Sankhya A (2020) 82: 1. https://doi.org/10.1007/s13171-018-00162-z | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 94480 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 04 Apr 2019 23:20 | |||||||||
| Last Modified: | 16 Nov 2021 17:05 |
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