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Chung-Type Strong Laws and Almost Complete Convergence for Arrays of Measurable Operators

Author

Listed:
  • Do The Son

    (Lam Son High School for the Gifted)

  • Duong Xuan Giap

    (Vinh University)

  • Nguyen Van Quang

    (Vinh University)

Abstract

The aim of this study is to establish some Chung-type strong laws of large numbers and almost complete convergence for arrays of measurable operators under various conditions. Some related results in the literature are extended to the noncommutative context.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01108-2
    DOI: 10.1007/s10959-021-01108-2
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    References listed on IDEAS

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    1. Tien-Chung Hu & R. L. Taylor, 1997. "On the strong law for arrays and for the bootstrap mean and variance," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-8, January.
    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. Robert Lee Taylor, 1983. "Complete convergence for weighted sums of arrays of random elements," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-11, January.
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