Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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C-DUNFORD INTEGRAL AND C-PETTIS INTEGRAL

  • Zhao, Dafang (Department of Mathematics Hubei Normal University) ;
  • You, Xuexiao (Department of Mathematics Hubei Normal University)
  • Received : 2007.11.13
  • Published : 2008.03.31
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Abstract

In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We prove that a function f is C-Dunford integrable if and only if $x^*f$ is C-integrable for each $x^*{\in}X^*$ and prove the controlled convergence theorem for the C-Pettis integral.

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