ON SOME PROPERTIES OF THE FUNCTION SPACE M

Let M be the vector space of all real S-measurable functions defined on a measure space (X, S, $\mu$). In this paper, we investigate some topological structure of T on M. Indeed, (M, T) becomes a topological vector space. Moreover, if $\mu$, is ${\sigma}-finite$, 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.