• East Asian mathematical journal
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• v.24 no.2
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• pp.201-212
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• 2008

We characterize operators between Banach spaces sending unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure of bounded variation. Further, we describe operators between Banach spaces taking unconditionally weakly p-summable sequences into sequences that lie in the range of a vector measure.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.525-531
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• 2007

We newly introduce the concept of summable in measure and investigate on some its properties. In addition to this, we consider a size of given series by means of we are giving Lebesgue measure to an associated series.

• Korean Journal of Mathematics
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• v.17 no.1
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• pp.37-41
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• 2009

We would like to propose Dirichlet-Jordan theorem on the space of summable in measure(SIM). Surely, this is a kind of extension of bounded variation([1, 4]), and considered as an application of fuzzy set such that ${\alpha}$-cut is 0.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.121-134
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• 2021

In this paper we introduce the notion of paranormed p-absolutely convergent and paranormed Cesro summable sequences of complex uncertain variables with respect to measure, mean, distribution etc. defined by on Orlicz function. We have established some relationships among these notions as well as with other classes of complex uncertain variables.

• Korean Journal of Mathematics
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• v.15 no.1
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• pp.13-26
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• 2007

We prove that every strong null sequence in a Banach space X lies inside the range of a vector measure of bounded variation if and only if the condition $\mathcal{N}_1(X,{\ell}_1)={\Pi}_1(X,{\ell}_1)$ holds. We also prove that for $1{\leq}p<{\infty}$ every strong ${\ell}_p$ sequence in a Banach space X lies inside the range of an X-valued measure of bounded variation if and only if the identity operator of the dual Banach space $X^*$ is ($p^{\prime}$,1)-summing, where $p^{\prime}$ is the conjugate exponent of $p$. Finally we prove that a Banach space X has the property that any sequence lying in the range of an X-valued measure actually lies in the range of a vector measure of bounded variation if and only if the condition ${\Pi}_1(X,{\ell}_1)={\Pi}_2(X,{\ell}_1)$ holds.