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ON SOME PROPERTIES OF THE FUNCTION SPACE

Let M be the vector space of all real S-measurable functions defined on a measure space (X,S, μ). In this paper, we investigate some topological structure of T on M. Indeed, (M, T ) becomes a topological vector space. Moreover, if μ is σ-finite, we can define a complete invariant metric on M which is compatible with the topology T on M, and hence (M, T ) becomes a F -space.