• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.73-79
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• 2002

In this paper, We Characterize the Pettis integrability for the Dunford integrable functions on a perfect finite measure space.

• Korean Journal of Mathematics
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• 제5권2호
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• pp.195-198
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• 1997

In this paper, we have some characterizations of Pettis integrability of bounded weakly measurable function $f:{\Omega}{\rightarrow}X^*$ determined by separable subspace of $X^*$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제3권1호
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• pp.1-7
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• 1996

Since the invention of the Pettis integral over half century ago, the problem of recognizing the Pettis integrability of a function against an individual condition has been much studied [1,6,7,8,12]. In spite of the R.F. Geitz (1982) and M. Talagrand's (1984) characterization of Pettis integrability, there is often trouble in recognizing when a function is or is not Pettis integrable.(omitted)

• 대한수학회논문집
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• 제15권1호
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• pp.91-102
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• 2000

In this paper we generalize some results of R. A. Gordon ([4]) and J. L. Garmez and J. Mendoza ([3]) and prove some convergence theorems for Denjoy-Dunford and Denjoy-Pettis integrable functions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제6권2호
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• pp.53-58
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• 1999

In this paper, we introduce the notion of separable-like function, investigate some properties of separable-like functions, and characterize the Pettis integrability of function on a finite perfect measure space.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권1호
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• pp.1-8
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• 1995

Since the concept of Pettis integral was introduced in 1938 [10], the Pettis integrability of weakly measurable functions has been studied by many authors [5, 6, 7, 8, 9, 11]. It is known that there is a bounded function that is not Pettis integrable [10, Example 10. 8]. So it is natural to raise the question: when is a bounded function Pettis integrable\ulcorner(omitted)

• East Asian mathematical journal
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• 제6권2호
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• pp.145-153
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• 1990

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권2호
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• pp.87-99
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• 2001

In this paper, we define the Mcshane-Stieltjes integral for Banach-valued functions, and will investigate some of its properties and comparison with the Pettis integral.

• 한국수학교육학회지시리즈A:수학교육
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• 제33권1호
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• pp.103-114
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• 1994

• 충청수학회지
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• 제8권1호
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• pp.111-117
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• 1995

A function $f:{\Omega}{\rightarrow}X$ is called intrinsically-separable valued if there exists $E{\in}{\Sigma}$ with ${\mu}(E)=0$ such that $f({\Omega}-E)$ is a separable in X. For a given Dunford integrable function $f:{\Omega}{\rightarrow}X$ and a weakly compact operator T, we show that if f is intrinsically-separable valued, then f is Pettis integrable, and if there exists a sequence ($f_n$) of Dunford integrable and intrinsically-separable valued functions from ${\Omega}$ into X such that for each $x^*{\in}X^*$, $x^*f_n{\rightarrow}x^*f$ a.e., then f is Pettis integrable. We show that a function f is Pettis integrable if and only if for each $E{\in}{\Sigma}$, F(E) is $weak^*$-continuous on $B_{X*}$ if and only if for each $E{\in}{\Sigma}$, $M=\{x^*{\in}X^*:F(E)(x^*)=O\}$ is $weak^*$-closed.