Some Kinds of Uniform Integrability and Laws of Large Numbers in Noncommutative Probability

Nguyen Quang (), Do The Son () and Le Hong Son ()
Additional contact information
Nguyen Quang: Vinh University
Do The Son: Industrial University of Ho Chi Minh City
Le Hong Son: Vinh University of Technology Education

Journal of Theoretical Probability, 2018, vol. 31, issue 2, 1212-1234

Abstract: Abstract The aim of this paper is to propose some equivalent conditions of uniform integrability for a sequence of measurable operators. Based on this result, we introduce some kinds of Cesàro uniform integrability in noncommutative probability. In addition, several results on the laws of large numbers related to these notions are established. Our results not only generalize related previously reported results but also improve them.

Keywords: Uniform integrability; Law of large numbers; Measurable operator; von Neumann algebra; Bilateral almost uniform convergence; 46L53; 60F15; 60F25 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-017-0740-x

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