• 제목/요약/키워드: equiintegrable

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THE H1-STIELTJES INTEGRAL OF BANACH-VALUED FUNCTIONS

  • Yoon, Ju Han;Park, Jae Myung;Lee, Deok Ho
    • 충청수학회지
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    • 제21권1호
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    • pp.49-56
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    • 2008
  • In this paper, we define the $H_1$ - Stieltjes integral of Banach-valued functions which is a generalization of real-valued $H_1$ - Stieltjes integral and investigate some properties of $H_1$ - Stieltjes integral. Also we show that if $f:[a,b]{\rightarrow}X$ be a function with ${\dim}X\;<\;{\infty}$, then $f{\in}H_1LS([a,b],X,{\alpha})$ if and only if $f{\in}H_1S([a,b],X,{\alpha})$.

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