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On the order structure of Orlicz lattices. (English) Zbl 0767.46005
Summary: We investigate the order structure of $$\delta$$-Dedekind complete Riesz spaces $$X$$ on which some functional $$\rho$$ called a modular is defined. The pairs $$(X,\rho)$$ will be called Orlicz lattices. Some additional conditions relating properties of $$\rho$$ to the order structure of $$X$$ are considered. Under these conditions imposed on $$\rho$$, we give some characterizations of sequential order convergence, sequential order star- convergence and order boundedness in $$X$$ in terms of the modular $$\rho$$.

##### MSC:
 46A80 Modular spaces 46A40 Ordered topological linear spaces, vector lattices 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)