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In this paper, we generalize a recently obtained result by Kopaliani andZviadadze from the one-variable case to the several-variable case.Specifically, in terms of decreasing rearrangement, we characterize thoseexponents $p(\cdot)$ for which the corresponding variable-exponent Lebesguespace $L^{p(\cdot)}([0;1]^n)$ shares the property with $L^\infty([0;1]^n)$ suchthat the space of continuous functions $C([0;1]^n)$ forms a closed linearsubspace in $L^{p(\cdot)}([0;1]^n)$ . In particular, we derive the necessaryand sufficient conditions on the decreasing rearrangement of the exponent$p(\cdot)$ for which there exists an equimeasurable exponent of $p(\cdot)$ suchthat the corresponding variable-exponent Lebesgue space possesses theaforementioned property.

The Note on the Closure of Continuous Functions in Variable-Exponent Lebesgue Spaces for Multiple Variables