Continuity of the Visibility Function in the Boundary
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 |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00465755_v80_n1-3_p43_PiacquadioLosada |
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| 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. In a recent paper, the present authors extended this characterization to compact subsets of Ed with certain topological restrictions. These restrictions are removed here and it is proved that the visibility function of a compact subset of Ed is continuous at a point if and only if the set of restricted visibility of this point has null Lebesgue outer measure. |
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