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A new and simple proof of the main result of the paper “Laterally closed lattice homomorphisms” by Toumi and Toumi (J Math Anal Appl 324:1178–1194, 2006) is given following the paper “Extension of Riesz homomorphisms, I” by Buskes (J Aust Math Soc Ser A 39(1):107–120, 1985).
The concept of a quasi-martingale is generalised to the Riesz space setting. Here we show that a quasi-martingale can be decomposed into the sum of a martingale and a quasi-potential. If, in addition, the quasi-martingale and its filtration are right continuous we show that the quasi-martingale can decomposed into the sum of a right continuous martingale and the difference of two positive right continuous...
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