ON SOME PROPERTIES OF THE FUNCTION SPACE M

Title & Authors
ON SOME PROPERTIES OF THE FUNCTION SPACE M
Lee, Joung-Nam;

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