On a Closed Subspace of ? ? ? ?

In this study, we first give a description of? ?? ?p .L ?spaces. These spaces are an important generalization ofclassical Lebesgue spaces. We mention their various applications in engineering and physics fields. Thereafter,as it is naturally, one of the main task in? ?? ?p .L ?spaces is to generalize known properties classical Lebesguespaces? ?pL ?to? ?? ?p .L ?spaces. Provided that measure of the set?is finite, we extend a theorem whichabout a closed subspace of? ?? ?p .L ?space, from constant exponent to variable exponent. Our proof method basedon embedding between? ?? ?p .L ? - ? ?pL ?spaces and the proof of constant case. The essence of the method isto take advantage of properties of Hilbert space? ?2L ?, and also based on the use of the closed graph theoremand finite measure of the set? .