  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].
