• Korean Journal of Mathematics
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• v.4 no.2
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• pp.89-94
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• 1996

In this paper we prove that for functions from [0,1] into a totally ordered AL-space, Mcshane integrability and absolute Mcshane integrability are equivalent.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.643-652
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• 2003

In this paper we introduce the concepts of the Mc-Shane-Stieltjes integral and the Denjoy-McShane-Stieltjes integral for Banach-valued functions and give a characterization of the Mc-Shane-Stieltjes integrability and investigate some properties of the Denjoy-McShane-Stieltjes integral.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.791-803
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• 2021

Earlier investigators have made detailed studies of geometric properties such as integrability, partial integrability, and invariants, such as the fundamental 2-form, of some canonical f-structures, such as f³ ± f = 0, on the frame bundle FM. Our aim is to study metallic structures on the frame bundle: polynomial structures of degree 2 satisfying F² = pF +qI where p, q are positive integers. We introduce a tensor field F_α, α = 1, 2…, n on FM show that it is a metallic structure. Theorems on Nijenhuis tensor and integrability of metallic structure F_α on FM are also proved. Furthermore, the diagonal lifts g^D and the fundamental 2-form Ω_α of a metallic structure F_α on FM are established. Moreover, the integrability condition for horizontal lift F_α^H of a metallic structure F_α on FM is determined as an application. Finally, the golden structure that is a particular case of a metallic structure on FM is discussed as an example.

• The Pure and Applied Mathematics
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• v.9 no.1
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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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• v.5 no.2
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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 $X^*$.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.407-415
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• 2011

We establish strong laws of large numbers for weighted sums of arrays of negatively associated random variables under the condition of h-integrability and suitable conditions on the array of weights.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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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.

• The Pure and Applied Mathematics
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• v.6 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1101-1111
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• 2008

Under the condition of h-integrability and appropriate conditions on the array of weights, we establish complete convergence and strong law of large numbers for weighted sums of an array of dependent random variables.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.591-602
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• 2012

In present paper we establish conditions for the integrability of various distributions of GCR-lightlike submanifolds and obtain conditions for the distributions to define totally geodesic foliations in GCR-lightlike submanifolds.