국가지식-학술정보
ON SOME PROPERTIES OF BOUNDED $X^{*}$-VALUED FUNCTIONS
ON SOME PROPERTIES OF BOUNDED $X^{*}$-VALUED FUNCTIONS
- 한국수학교육학회
- The Pure and Applied Mathematics
- Vol.1 No.1
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1994.0125 - 27 (3 pages)
- 0
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Suppose that X is a Banach space with continuous dual $X^{**}$, ($\Omega$, $\Sigma$, ${\mu}$) is a finite measure space. f : $\Omega\;{\longrightarrow}$ $X^{*}$ is a weakly measurable function such that $\chi$$^{**}$ f $\in$ $L_1$(${\mu}$) for each $\chi$$^{**}$ $\in$ $X^{**}$ and $T_{f}$ : $X^{**}$ \longrightarrow $L_1$(${\mu}$) is the operator defined by $T_{f}$($\chi$$^{**}$) = $\chi$$^{**}$f. In this paper we study the properties of bounded $X^{*}$ - valued weakly measurable functions and bounded $X^{*}$ - valued weak＊ measurable functions.(omitted)
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