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A Uniform Convergence Theorem for Approximate Henstock-Stieltjes Integral
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Abstract
In this paper, we introduce, for each approximate distributiontilt of [a,b], the approximate Henstock-Stieltjes integralwith value in Banach spaces. The Henstock integral is a specialcase of this where tilt={(tau,[a,b]): tauin[a,b]}. Thisnew concept generalizes Henstock integral and abstractPerron-Stieltjes integral. We establish a uniform convergencetheorem for approximate Henstock-Stieltjes integral, which is animprovement of the uniform convergence theorem forPerron-Stieltjes integral by Schwabik [3].
참고문헌 (4)
- "The integrals of Lebesgue" (1994)
- "Lectures on the theory of integration}" (1988)
- "emph{Abstract Perron-Stieltjes integral},", 121(4), pp.425~447 (1996)
- "emph{Abstract Perron-Stieltjes integral}", 121(4), pp.425~447 (1996)
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