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Equivalence of the ap-Sequential Henstock and ap-Sequential Topological Henstock Integrals
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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.
Title: Equivalence of the ap-Sequential Henstock and ap-Sequential Topological Henstock Integrals
Description:
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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