• Korean Journal of Mathematics
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• 제11권2호
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• pp.137-146
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• 2003

In this paper we introduce the concepts of the weak $Denjoy_*$ integral of real-valued functions and the weak $Denjoy_*$-Dunford, weak $Denjoy_*$-Pettis, weak $Denjoy_*$-Bochner, weak $Denjoy_*$-McShane integrals of Banach-valued functions and then investigate some of their properties.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권3호
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• pp.315-327
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• 2008

In this paper we introduce the concepts of $Denjoy_*$-Stieltjes-Dunford, $Denjoy_*$-Stieltjes-Pettis, $Denjoy_*$-Stieltjes-Bochner and $Denjoy_*$-McShane-Stieltjes integrals of Banach-valued functions using the $Denjoy_*$-Stieltjes integral of real-valued functions and investigate their properties.

• 충청수학회지
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• 제23권4호
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• pp.879-884
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• 2010

In this paper, we introduce the AP-Henstock Dunford, AP-Henstock Pettis and AP-Henstock Bochner integral Banach-valued functions and investigate some properties of the these integrals.

• 충청수학회지
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• 제17권2호
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• pp.147-162
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• 2004

In this paper, we investigate the relations between the McShane and Pettis integrals.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.87-92
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• 1997

Some function of a complete finite measure space (for short, CFMS) into the duals and pre-duals of weakly compactly generated (for short, WCG) spaces are considered. We shall show that a universally weakly measurable function f of a CFMS into the dual of a WCG space has RS property and bounded weakly measurable functions of a CFMS into the pre-duals of WCG spaces are always Pettis integrable.

• 대한수학회지
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• 제55권4호
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• pp.833-848
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• 2018

In this paper we study the existence of conditional expectation for closed and convex valued Pettis-integrable random sets without assuming the Radon Nikodym property of the Banach space. New version of multivalued dominated convergence theorem of conditional expectation and multivalued $L{\acute{e}}vy^{\prime}s$ martingale convergence theorem for integrable and Pettis integrable random sets are proved.

• 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)

• 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)

• 대한수학회지
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• 제57권2호
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• pp.359-381
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• 2020

In this paper we established new results of existence of conditional expectation for closed convex and unbounded Pettis integrable random sets without assuming the Radon Nikodym property of the Banach space. As application, new versions of multivalued Lévy's martingale convergence theorem are proved by using the Slice and the linear topologies.

• 대한수학회보
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• 제33권2호
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• pp.277-287
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• 1996

The theory of integration of functions with values in a Banach space has long been a fruitful area of study. In the eight years from 1933 to 1940, seminal papers in this area were written by Bochner, Gelfand, Pettis, Birhoff and Phillips. Out of this flourish of activity, two integrals have proved to be of lasting: the Bochner integral of strongly measurable function. Through the forty years since 1940, the Bochner integral has a thriving prosperous history. But unfortunately nearly forty years had passed until 1976 without a significant improvement after B. J. Pettis's original paper in 1938 [cf. 11].