PIMS - ULethbridge Distinguished Speaker: Vladimir Troitsky

In this talk, we will discuss order convergence and unbounded order convergence (uo-convergence) on vector lattices. In many classical function spaces, uo-convergence agrees with almost everywhere convergence. Thus, uo-convergence may be viewed as a generalization of almost everywhere convergence from function spaces to general vector lattices. This leads to extensions of several classical theorems from function spaces to vector lattice setting, including Doob's martingale convergence theorem and Komlos' theorem about convergence of Cesaro averages. We will also discuss whether uo-convergence is stable under passing to a sublattice.