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Some general strong laws of large numbers for sequence of measurable operators

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  • Quang, Nguyen Van
  • Talebi, Ali

Abstract

In this paper, we establish some general laws of large numbers for sequence of measurable operators such that several known strong law of large numbers (LLN) in von Neumann algebras. One of our main achievements extends the main result of Jajte (2003) in some senses such that Batty’s strong LLN and Łuczak’s result are obtained as special cases. The result is new even in the case of classical random variables.

Suggested Citation

  • Quang, Nguyen Van & Talebi, Ali, 2026. "Some general strong laws of large numbers for sequence of measurable operators," Statistics & Probability Letters, Elsevier, vol. 227(C).
    • Handle: RePEc:eee:stapro:v:227:y:2026:i:c:s0167715225001968
    DOI: 10.1016/j.spl.2025.110551
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    References listed on IDEAS

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    1. Do The Son & Duong Xuan Giap & Nguyen Van Quang, 2022. "Chung-Type Strong Laws and Almost Complete Convergence for Arrays of Measurable Operators," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1391-1411, September.
    2. Nguyen Quang & Do The Son & Le Hong Son, 2018. "Some Kinds of Uniform Integrability and Laws of Large Numbers in Noncommutative Probability," Journal of Theoretical Probability, Springer, vol. 31(2), pages 1212-1234, June.
    3. Yu Miao & Jianyong Mu & Shuili Zhang, 2020. "Limit theorems for identically distributed martingale difference," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(6), pages 1435-1445, March.
    4. Stoica, George, 2009. "Noncommutative Baum-Katz theorems," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 320-323, February.
    5. Rosalsky, Andrew & Thành, Lê Vǎn, 2021. "A note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 178(C).
    6. Soo Hak Sung, 2014. "Marcinkiewicz–Zygmund Type Strong Law of Large Numbers for Pairwise i.i.d. Random Variables," Journal of Theoretical Probability, Springer, vol. 27(1), pages 96-106, March.
    7. Cuculescu, I., 1971. "Martingales on von Neumann algebras," Journal of Multivariate Analysis, Elsevier, vol. 1(1), pages 17-27, April.
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