In this paper, we extend several classical probability inequalities to the Riesz space setting. We provide Marshall’s inequality in Riesz spaces. The Marshall’s inequality is stronger than the Kolmogorov’s inequality. It gives a bound on the probability for the partial sums of a sequence of independent random variables. Also, we state an inequality of maximal increment in Riesz space which known as Shao inequality. In addition, we find a better estimate for Etemadi’s inequality in vector lattices. Furthermore we establish weak symmetrization inequalities and Strong symmetrization inequalities in the framework of measure-free. In the weak symmetrization inequalities we state the relation between tail probabilities of random variables and tail probabilities of their symmetrizations. In the Strong symmetrization inequalities we extend the weak symmetrization inequalities to the maximal inequalities.
Divandar, M. S. & Sadeghi, G. (2027). Some probability inequalities in Riesz spaces. Journal of Frame and Matrix Theory, 3(1), 20–36. https://doi.org/10.22034/jfmt.2026.558228.1031
MLA
Divandar, M. S., & Sadeghi, G. "Some probability inequalities in Riesz spaces", Journal of Frame and Matrix Theory, 3, 1, 2027, 20–36. doi: 10.22034/jfmt.2026.558228.1031
HARVARD
Divandar, M. S., & Sadeghi, G. (2027). 'Some probability inequalities in Riesz spaces', Journal of Frame and Matrix Theory, 3(1), pp. 20–36. doi: 10.22034/jfmt.2026.558228.1031
CHICAGO
Divandar, M. S. & Sadeghi, G., "Some probability inequalities in Riesz spaces." Journal of Frame and Matrix Theory, 3 1 (2027): 20–36, doi: 10.22034/jfmt.2026.558228.1031
VANCOUVER
Divandar M. S., Sadeghi G. Some probability inequalities in Riesz spaces. JFMT. 2027;3(1):20–36. doi: 10.22034/jfmt.2026.558228.1031
