The task of integral geometry with measure induction

Abstract

A new statement of Integral Geometry problem where the image of function in each point is taken as an integral with respect to measure which depends on the point is suggested. Such Measure System is named Measure Induction. It is shown that an inversion formula exists for class of measures having a unit atom in correspondingpoint and limited on whole space. Previously obtained results for average on systems of measurement dissections and for weight average on graphs are generalized.

Keywords

• integral geometry
• measure
• functional space
• linear operators
• inversion formulas