# ON SOME PROPERTIES OF THE FUNCTION SPACE M

Lee, Joung-Nam

• Published : 2003.10.01
• 56 3

#### Abstract

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.

#### Keywords

${\mu}-equivalent$;${\sigma}-finite$ measure;S-measurable function;F-space

#### References

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