An approach to F. Riesz representation Theorem
Author
del Rio, Rafael
Franco, Asaf L.
Lara, Jose A.
Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/204510.4067/S0719-06462018000200001
Abstract
In this note we give a direct proof of the F. Riesz representation theorem which characterizes the linear functionals acting on the vector space of continuous functions defined on a set K. Our start point is the original formulation of Riesz where K is a closed interval. Using elementary measure theory, we give a proof for the case K is an arbitrary compact set of real numbers. Our proof avoids complicated arguments commonly used in the description of such functionals.