Geodesic
The Continuity of the Visibility Function on a Starshaped Set
Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 989-992

Voir la notice de l'article provenant de la source Cambridge University Press

The visibility function assigns to each point x of a fixed measurable set E in a Euclidean space En the Lebesgue outer measure of S(x), the set {y : rx + (1 — r)y ∊ E for every r in [0, 1]}.The purpose of this paper is to determine sufficient conditions for the continuity of the function on the interor of a starshaped set. 
Beer, Gerald. The Continuity of the Visibility Function on a Starshaped Set. Canadian journal of mathematics, Tome 24 (1972) no. 5, pp. 989-992. doi: 10.4153/CJM-1972-100-7
@article{10_4153_CJM_1972_100_7,
     author = {Beer, Gerald},
     title = {The {Continuity} of the {Visibility} {Function} on a {Starshaped} {Set}},
     journal = {Canadian journal of mathematics},
     pages = {989--992},
     year = {1972},
     volume = {24},
     number = {5},
     doi = {10.4153/CJM-1972-100-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-100-7/}
}
TY  - JOUR
AU  - Beer, Gerald
TI  - The Continuity of the Visibility Function on a Starshaped Set
JO  - Canadian journal of mathematics
PY  - 1972
SP  - 989
EP  - 992
VL  - 24
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-100-7/
DO  - 10.4153/CJM-1972-100-7
ID  - 10_4153_CJM_1972_100_7
ER  - 
%0 Journal Article
%A Beer, Gerald
%T The Continuity of the Visibility Function on a Starshaped Set
%J Canadian journal of mathematics
%D 1972
%P 989-992
%V 24
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1972-100-7/
%R 10.4153/CJM-1972-100-7
%F 10_4153_CJM_1972_100_7

[1] 1. Gerald, Beer, The index of convexity and the visibility function (to appear in Pacific J. Math.). Google Scholar

[2] 2. Gerald, Beer, Continuity properties of the visibility function (to appear). Google Scholar

[3] 3. Valentine, F. A., Convex sets (McGraw-Hill, New York, 1964). Google Scholar

Cité par Sources :