Based on the properties of indicator function and the theory of Lebesgue-Stieljes integral,we provided another method to prove Jordan formula and measure infer(super) limit inequality.

The indicator function and its properties are discussed in this paper.

The Application of Indicate Function in Mathematics expectation and Method difference;

Examples show the applications of indicate function in actuarial techniques.

First, the fundamental equation is set up, and, direct and inverse scattering problem are discussed; Second, indicator function of represent scatterer characterization is constructed; Third, the boundary of scatterer is determined by property of the function.

First,the indicator function representing the scattering characteristics is constructed;then,based on the property of the function,the fundamental equation for solving the inverse problem is established;thereby,the shape of the obstacle is determined.

Some relationships among the support function and indicator function of a convex set and their second-order epi-derivatives are given.

With indicator function,support function,distance function,and projection of a point to a closed convex body,the canonical representation for a convex body and characterization on the projection of a point to boundary of the set are presented.