In this note it is shown that the $L^1$-bounded uniform amarts in $l^1$ form a vector lattice. This extends a result of Austin, Edgar and Ionescu Tulcea on real-valued $L^1$-bounded amarts and parallels a result of Ghoussoub on $L^1$-bounded order amarts.
"The Lattice Property of Uniform Amarts." Ann. Probab. 17 (1) 372 - 378, January, 1989. https://doi.org/10.1214/aop/1176991516