序贯Henstock积分与序贯拓扑Henstock积分的等价性

V. O. Iluebe, Adesanmi Alao Mogbademu
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引用次数: 0

摘要

设$X$为拓扑空间,$\Omega \subset X$。假设$f:\Omega\rightarrow X$是在完整空间$ \Omega $中定义的函数,$ \tau $是$ \mathbb{R} $中的矢量,其值在$X$中。假设$ f $是ap-顺序Henstock对$\tau$可积,$ f $ ap-顺序Henstock对$\tau$可积吗?本文的目的是为这个问题提供肯定的答案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Equivalence of the ap-Sequential Henstock and ap-Sequential Topological Henstock Integrals
Let $X$ be a topological space and $\Omega \subset X$. Suppose $f:\Omega\rightarrow X$ is a function defined in a complete space $ \Omega $ and $ \tau $ is a vector in $ \mathbb{R} $ taking values in $X$. Suppose $ f $ is ap-Sequential Henstock integrable with respect to $\tau$, is $ f $ ap-Sequential Topological Henstock integrable with respect to $\tau$? It is the purpose of this paper to proffer affirmative answer to this question.
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