Delta连续Stieltjes变分在平面上的积分
Integration of Delta Continuous Stieltjes Variational in the Plane
摘要：
本文讨论了平面上推广的δ连续Stieltjes变分积分。特别地，本文给出了它的一些基本性质，并将平面上δ连续的Stieltjes变分积分看作是定义在实直线上的同类积分的推广形式[4]。定义在实直线上和平面上的δ连续Stieltjes变分积分的极大差异与它们的原函数有关。其中，如果$F$是定义在实直线上的δ连续Stieltjes变分可积$f$的原函数，则$F$是点函数。同时，在平面中，函数$F$被视为区间函数。因此，为了研究δ连续Stieltjes变分在平面上的积分的性质，通常需要以前出现的一些想法（见1。[4]中所没有的。
英文摘要：
This paper deals with the delta continuous Stieltjes variational integral generalized in the plane. In particular, this work presents about some fundamental properties of it. The delta continuous Stieltjes variational integral in the plane is considered as a form of generalization of the same type of integral defined in the real line [4]. The extremely difference between the delta continuous Stieltjes variational integrals defined in both the real line and the plane is especially related to their primitive functions. Where, if $F$ is a primitive function of the delta continuous Stieltjes variational integrable $f$ defined on the real line, then $F$ is a point function. Meanwhile, in the plane the function $F$ is looked at as an interval function. Therefore, in order to investigate the properties of the integration of delta continuous Stieltjes variational in the plane is often needed some ideas appeared previously (see 1. Introduction) which are not available in [4].
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