The visibility function revisited

The visibility function of a compact set S ⊂ Ed assigns to each x ∈ S the Lebesgue outer measure of its star in S. This function was introduced by G. Beer in 1972. In 1991, A. Forte Cunto characterized the points of discontinuity of the visibility function in the boundary of a planar Jordan domain....

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Autor principal: Toranzos, Fausto Alfredo
Publicado: 1999
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00472468_v65_n1-2_p101_Cunto
http://hdl.handle.net/20.500.12110/paper_00472468_v65_n1-2_p101_Cunto
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00472468_v65_n1-2_p101_Cunto
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spelling paper:paper_00472468_v65_n1-2_p101_Cunto2023-06-08T15:05:33Z The visibility function revisited Toranzos, Fausto Alfredo The visibility function of a compact set S ⊂ Ed assigns to each x ∈ S the Lebesgue outer measure of its star in S. This function was introduced by G. Beer in 1972. In 1991, A. Forte Cunto characterized the points of discontinuity of the visibility function in the boundary of a planar Jordan domain. The basic intention of this paper is to extend this characterization to a compact subset of Ed. Under certain assumptions, it is proved here that the visibility function of such a set is continuous at a point if and only if the set of restricted visibility of this point has null Lebesgue outer measure. © Birkhäuser Verlag, 1999. Fil:Toranzos, F.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1999 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00472468_v65_n1-2_p101_Cunto http://hdl.handle.net/20.500.12110/paper_00472468_v65_n1-2_p101_Cunto
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description The visibility function of a compact set S ⊂ Ed assigns to each x ∈ S the Lebesgue outer measure of its star in S. This function was introduced by G. Beer in 1972. In 1991, A. Forte Cunto characterized the points of discontinuity of the visibility function in the boundary of a planar Jordan domain. The basic intention of this paper is to extend this characterization to a compact subset of Ed. Under certain assumptions, it is proved here that the visibility function of such a set is continuous at a point if and only if the set of restricted visibility of this point has null Lebesgue outer measure. © Birkhäuser Verlag, 1999.
author Toranzos, Fausto Alfredo
spellingShingle Toranzos, Fausto Alfredo
The visibility function revisited
author_facet Toranzos, Fausto Alfredo
author_sort Toranzos, Fausto Alfredo
title The visibility function revisited
title_short The visibility function revisited
title_full The visibility function revisited
title_fullStr The visibility function revisited
title_full_unstemmed The visibility function revisited
title_sort visibility function revisited
publishDate 1999
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00472468_v65_n1-2_p101_Cunto
http://hdl.handle.net/20.500.12110/paper_00472468_v65_n1-2_p101_Cunto
work_keys_str_mv AT toranzosfaustoalfredo thevisibilityfunctionrevisited
AT toranzosfaustoalfredo visibilityfunctionrevisited
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