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.
@article{2045,
title = {An approach to F. Riesz representation Theorem},
journal = {CUBO, A Mathematical Journal},
volume = {20},
year = {2018},
doi = {10.4067/S0719-06462018000200001},
language = {en},
url = {http://dml.mathdoc.fr/item/2045}
}
del Rio, Rafael; Franco, Asaf L.; Lara, Jose A. An approach to F. Riesz representation Theorem. CUBO, A Mathematical Journal, Tome 20 (2018) . doi : 10.4067/S0719-06462018000200001. http://gdmltest.u-ga.fr/item/2045/