منابع مشابه
Translative and kinematic integral formulae concerning the convex hull operation
exists and can be expressed in terms of K and K ′. The functionals F under consideration are derived from the mixed volume or the mixed area measure functional. Analogous questions are treated for the motion group instead of the translation group. The resulting relations can be regarded as dual counterparts to various versions of the principal kinematic formula. Motivation for our investigation...
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For simplicity, we follow the rules: X denotes a non empty set, Y denotes a set, S denotes a σ-field of subsets of X, F denotes a function from N into S, f , g denote partial functions from X to R, A, B denote elements of S, r, s denote real numbers, a denotes a real number, and n denotes a natural number. Let X be a non empty set, let f be a partial function from X to R, and let a be a real nu...
متن کاملTranslative and Kinematic Integral Formulae concerning the Convex Hull Operation Translative and Kinematic Integral Formulae
For convex bodies K; K 0 and a translation in n-dimensional Euclidean space, let K _ K 0 be the convex hull of the union of K and K 0. Let F be a geometric functional on the space of all convex bodies. We consider special families (r) r>0 of measures on the translation group T n such that the limit lim r!1 Z Tn F (K _ K 0) dd r () exists and can be expressed in terms of K and K 0. The functiona...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1975
ISSN: 0022-247X
DOI: 10.1016/0022-247x(75)90009-8