An approach to F. Riesz representation Theorem
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Rafael del Rio
delrio@iimas.unam.mx
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Asaf L. Franco
asaflevif@hotmail.com
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Jose A. Lara
nekrotzar.ligeti@gmail.com
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DOI:
https://doi.org/10.4067/S0719-06462018000200001Abstract
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.
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