• 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.

• 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.

• 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.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.749-763
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• 2018

In this paper firstly, It was studied almost paraholomorphic vector field with respect to almost para-Nordenian structure ($F^S$, g) and the purity conditions of the Sasakian metric is investigate with respect to almost para complex structure F on cotangent bundle. Secondly, we obtained the integrability conditions of almost paracomplex structure F by calculating the Nijenhuis tensors of F of type (1, 1) on $^CT(M_n)$. Finally, the Tachibana operator ${\phi}_{\varphi}$ applied to $^Sg$ according to F and the Vishnevskii operators (${\psi}_{\varphi}$-operator) applied to the vertical and horizontal lifts with respect to F on cotangent bundle.

• 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.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1097-1110
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• 2012

The convergence properties of extended negatively dependent sequences under some conditions of uniform integrability are studied. Some sufficient conditions of the weak law of large numbers, the $p$-mean convergence and the complete convergence for extended negatively dependent sequences are obtained, which extend and enrich the known results in the literature.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.73-90
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• 2012

We define a quarter-symmetric non-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a quarter-symmetric non-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.207-218
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• 2013

In this paper, we study GCR-lightlike submanifolds of indefinite Sasakian manifold. We give some necessary and sufficient conditions on integrability of various distributions of GCR-lightlike submanifold of an indefinite Sasakian manifold. We also find the conditions for each leaf of holomorphic distribution and radical distribution is totally geodesic.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.25-32
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• 2012

We define a quarter symmetric metric connection in a Lorentzia para-Sasakian manifold and study CR-submanifolds of a Lorentzian para-Sasakian manifold endowed with a quarter symmetric metric connection. Moreover, we also obtain integrability conditions of the distributions on CR-submanifolds.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1451-1473
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• 2020

Widely orthant dependence (WOD, in short) is a special dependence structure. In this paper, by using the probability inequalities and moment inequalities for WOD random variables, we study the L_p convergence and complete convergence for the partial sums respectively under the conditions of RCI(α), SRCI(α) and R-h-integrability. We also give an application to nonparametric regression models based on WOD errors by using the L_p convergence that we obtained. Finally we carry out some simulations to verify the validity of our theoretical results.