THE STATISTICAL MULTIPLICATIVE ORDER CONVERGENCE IN RIESZ ALGEBRAS

Abstract

The statistically multiplicative convergence in Riesz algebras was studied and investigated with respect to the solid topology. In the present paper, the statistical convergence with the multiplication in Riesz algebras is introduced by developing topology-free techniques using the order convergence in vector lattices. Moreover, we give some relations with the other kinds of convergences such as the order statistical convergence, the $mo$-convergence, and the order convergence.