Inequalities of the Chebyshev type based on pseudo-integrals

This paper presents the Chebyshev type of pseudo-integral inequalities, with the particular emphasis on the g-semirings. With the suitable choice of the generator g, the pseudo-expectation and pseudo-moments exist for the Cauchy distribution (in general case the standard expectation and moments for the Cauchy distribution are not defined). The computation of the pseudo-expectation for the Cauchy distribution and some examples that illustrate the applicability of the introduced generalization are also given in the paper.