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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| Autores principales: | , , |
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00472468_v65_n1-2_p101_Cunto |
| Aporte de: |
| Sumario: | 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. |
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