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ON SOME PROPERTIES OF THE FUNCTION SPACE M

Lee, Joung-Nam

  • Published : 2003.10.01

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

  1. The elements of real analysis(2nd ed.) R.G.Bartle
  2. Measure, Integration and Functional Analysis B.A.Robert
  3. J. Korea Soc. Math. Educ. v.33 A note on the function space Μ J.N.Lee
  4. The elements of integration R.G.Bartle
  5. Topology and maps T.Husain
  6. Topological vector spaces H.H.Schaefer
  7. Real analysis(2nd ed.) H.L.Royden
  8. General Theory of Functions and Integration A.E.Taylor