An approach to F. Riesz representation Theorem

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 me...

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Autores principales:	del Rio,Rafael, Franco,Asaf L., Lara,Jose A.
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2018
Materias:	Riesz representation theorem positive linear functionals RiemannStieltjes integral.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462018000200001
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spelling	oai:scielo:S0719-064620180002000012019-02-13An approach to F. Riesz representation Theoremdel Rio,RafaelFranco,Asaf L.Lara,Jose A. Riesz representation theorem positive linear functionals RiemannStieltjes integral. 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.20 n.2 20182018-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462018000200001en10.4067/S0719-06462018000200001
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Riesz representation theorem positive linear functionals RiemannStieltjes integral.
spellingShingle	Riesz representation theorem positive linear functionals RiemannStieltjes integral. del Rio,Rafael Franco,Asaf L. Lara,Jose A. An approach to F. Riesz representation Theorem
description	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.
author	del Rio,Rafael Franco,Asaf L. Lara,Jose A.
author_facet	del Rio,Rafael Franco,Asaf L. Lara,Jose A.
author_sort	del Rio,Rafael
title	An approach to F. Riesz representation Theorem
title_short	An approach to F. Riesz representation Theorem
title_full	An approach to F. Riesz representation Theorem
title_fullStr	An approach to F. Riesz representation Theorem
title_full_unstemmed	An approach to F. Riesz representation Theorem
title_sort	approach to f. riesz representation theorem
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2018
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462018000200001
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An approach to F. Riesz representation Theorem

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