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In this note some structural properties of grand variable exponent Lebesgue/Morrey spaces over spaces of homogeneous type are obtained. In particular, itis proved that the closure of the class of bounded functions and the closure ofclassical Morrey space in grand variable exponent Morrey space coincide if themeasure of the underlying space is finite. Moreover, we get two differentcharacterizations of this class. Further, duality and preduality of grandvariable exponent Lebesghue space defined on quasi-metric measure spaces withsigma-finite measure are obtained, which is new even when underlying measure isfinite.

Density, Duality and Preduality in Grand Variable Exponent Lebesgue and Morrey Spaces