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1. 

   A note on regular martingales in Riesz spaces

   Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Mareli Korostenski CoenraadC.A. Labuschagne

   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...

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2. 

   Doob's decomposition of set-valued submartingales via ordered near vector spaces

   Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: CoenraadC.A. Labuschagne AndrewL. Pinchuck

   We use ideas from measure-free martingale theory and Rådström's completion of a near vector space to derive a Doob decomposition of submartingales in ordered near vector spaces. As a special cases thereof, we obtain the Doob decomposition of set-valued submartingales,...

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