Kantorovich-Wright integration and representation of quasi-Banach lattices

The purpose of this article is to give some applications of the purely order based Kantorovich-Wright integration to functional representation of quasi-Banach lattices as well as to reveal its interrelations with the Bartle-Dunford-Schwartz topological integration. The special case of measures with values in order continuous quasi-Banach lattices when the two integration theories coincide is also examined.