Document Type : Original Article
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.
Department of Health, Torbat Heydariyeh University of Medical Sciences, Torbat Heydariyeh, Iran
We establish a maximal probability inequality for a class of random variables in the framework of measure-free, Riesz spaces. In the ``other" Kolmogorov's inequality, we consider an upper bound for independent random variables and estimate the lower bound for the sums of random variables in Riesz spaces setting. Furthermore, we get an upper bound for the variance of the sum of random variables.