A UNIFORM CONVERGENCE THEOREM FOR APPROXIMATE HENSTOCK-STIELTJES INTEGRAL

Title & Authors
A UNIFORM CONVERGENCE THEOREM FOR APPROXIMATE HENSTOCK-STIELTJES INTEGRAL
Im, Sung-Mo; Kim, Yung-Jinn; Rim, Dong-Il;

Abstract
In this paper, we introduce, for each approximate distribution $\small{\~{T}}$ of [a, b], the approximate Henstock-Stieltjes integral with value in Banach spaces. The Henstock integral is a special case of this where $\small{\~{T}\;=\;\{(\tau,\;[a,\;b])\;:\;{\tau}\;{\in}\;[a,\;b]\}}$. This new concept generalizes Henstock integral and abstract Perron-Stieltjes integral. We establish a uniform convergence theorem for approximate Henstock-Stieltjes integral, which is an improvement of the uniform convergence theorem for Perron-Stieltjes integral by Schwabik [3].
Keywords
bilinear triple;approximate distribution;approximate Henstock-Stieltjes integral;
Language
English
Cited by
References
1.
Amer. Math. Soc., Providence, 1994.

2.
Lectures on the theory of integration, 1988.

3.
Math. Bohem., 1996. vol.121. 4, pp.425-447