The ρ-Fatau property of lattice-normed vector lattices

In This note, we carry out investigations the necessary and sufficient condition for a certain non-empty subsets lattice-normed vector lattice to have one of the follwing properties : the order ρ-continuous and the ρ-Fatou property. We also give an examples of lattice-normed vector lattice decomposable whice is not have ρ-Fatou property.