Abstract
In this paper we characterize those exponents p ( ⋅ ) for which corresponding variable exponent Lebesgue space L p ( ⋅ ) ( [ 0 ; 1 ] ) has in common with L ∞ the property that the space of continuous functions is a closed linear subspace in it. In particular, we obtain necessary and sufficient condition on decreasing rearrangement of exponent p ( ⋅ ) for which exists equimeasurable exponent of p ( ⋅ ) which corresponding variable exponent Lebesgue space have the above mentioned property.
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