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We consider regular martingales (i.e., martingales which can be written as differences of two positive martingales) in the measure-free setting of Riesz spaces. The aim of this note is to show that the space of such martingales is a Riesz space. We derive an analogue of a result of Troitsky's on regular norm bounded martingales in Banach lattices.

Keywords: filtration; martingale; submartingale; Riesz space

Quaestiones Mathematicae 31(2008), 219–224