Density of Function in the Mathematical Analysis

Abstract

On the ground of the definition of arbitrary function of one argument and the mutual and unambiguous correspondence between the values of the function and argument, the following concepts have been deveined: 

1. Absolute average and differential linear density of the function and argument;
2. Relative linear density of one function toward another function;
3. Relative linear density of the argument of one function toward the argument of another function.

The conditions are shown under which these definitions apply: continuity and differentiability of the function; monotony of the function; equal quality of the arrays of values of argument and function and the examination has been done of the specified densities.

The generalization of the concepts of the density of function and argument has been done in the case of a function of two and three variables and the theorem on projections of vector quantity and tensor quantity on the co-ordinate axes and planes has been proven