Riemann-Stieltjes integration in Riesz spaces

Abstract

After introducing an integral for Riesz-space valued integral functions, this concept is used to represent the variation of a continuous function, to define integrals along a curve and Riemann-Stieltjes integrals, and to deduce from them, as particular cases, some kinds of stochastic integral.

Keywords

• riesz space
• (0)-convergence
• integration
• variation