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