Generalization of the theorems of Barndorff-Nielsen and Balakrishnan-Stepanov to Riesz spaces

Nyasha Mushambi, Bruce A. Watson, Bertin Zinsou

In a Dedekind complete Riesz space, $E$, we show that if $(P_n)$ is a sequence of band projections in $E$ then $$\limsup\limits_{n\to \infty} P_n - \liminf\limits_{n\to \infty} P_n…