Convex Sets and Subharmonicity of the Distance Function
نویسندگان
چکیده
منابع مشابه
Distance sets corresponding to convex bodies
Suppose that K ⊆ R, d ≥ 2, is a 0-symmetric convex body which defines the usual norm ‖x‖K = sup {t ≥ 0 : x / ∈ tK} on R. Let also A ⊆ R be a measurable set of positive upper density ρ. We show that if the body K is not a polytope, or if it is a polytope with many faces (depending on ρ), then the distance set DK(A) = {‖x− y‖K : x, y ∈ A} contains all points t ≥ t0 for some positive number t0. Th...
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15 صفحه اولConvex Sets and Convex Combinations
Convexity is one of the most important concepts in a study of analysis. Especially, it has been applied around the optimization problem widely. Our purpose is to define the concept of convexity of a set on Mizar, and to develop the generalities of convex analysis. The construction of this article is as follows: Convexity of the set is defined in the section 1. The section 2 gives the definition...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1988
ISSN: 0002-9939
DOI: 10.2307/2047169