共查询到20条相似文献,搜索用时 46 毫秒
1.
Johan Jonasson 《Journal of multivariate analysis》1998,65(2):129-138
Random objects taking on values in a locally compact second countable convex cone are studied. The convex cone is assumed to have the property that the class of continuous additive positively homogeneous functionals is separating, an assumption which turns out to imply that the cone is positive. Infinite divisibility is characterized in terms of an analog to the Lévy–Khinchin representation for a generalized Laplace transform. The result generalizes the classical Lévy–Khinchin representation for non-negative random variables and the corresponding result for random compact convex sets inRn. It also gives a characterization of infinite divisibility for random upper semicontinuous functions, in particular for random distribution functions with compact support and, finally, a similar characterization for random processes on a compact Polish space. 相似文献
2.
Beifang Chen 《Studies in Applied Mathematics》1994,91(1):39-50
This paper introduces Geissinger multiplication on the vector space generated by indicator functions of closed convex sets. Minkowski's mixed volume for compact convex sets is naturally represented in terms of the volume of the Geissinger multiplication of their indicator functions. Some properties of mixed volumes and new results are obtained by this representation, including a polynomial identity. 相似文献
3.
A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of compact elements. In particular, a semilattice Ω(η), that does not appear among minimal obstructions to order-scattered algebraic modular lattices, plays a prominent role in convex geometries case. The connection to topological scatteredness is established in convex geometries of relatively convex sets. 相似文献
4.
5.
We give a characterization of those compact sets in the plane with finitely many holes that are images of disk-algebra functions. We also show that the image of the closed unit disk via a polynomial is, in general, not polynomially convex. 相似文献
6.
Peter Kohlmann 《Geometriae Dedicata》1996,60(2):125-143
We consider noncompact, closed and convex sets with nonvoid interior in Euclidean space. It is shown that if such a set has one curvature measure sufficiently close to the boundary measure, then it is congruent to a product of a vector space and a compact convex body. Related stability and characterization theorems for orthogonal disc cylinders are proved. Our arguments are based on the Steiner-Schwarz symmetrization processes and generalized Minkowski integral formulas. 相似文献
7.
This paper investigates the closedness and convexity of the range sets of the variational inequality (VI) problem defined by an affine mappingM and a nonempty closed convex setK. It is proved that the range set is closed ifK is the union of a polyhedron and a compact convex set. Counterexamples are given such that the range set is not closed even ifK is a simple geometrical figure such as a circular cone or a circular cylinder in a three-dimensional space. Several sufficient conditions for closedness and convexity of the range set are presented. Characterization for the convex hull of the range set is established in the case whereK is a cone, while characterization for the closure of the convex hull of the range set is established in general. Finally, some applications to stability of VI problems are derived.This work was supported by the Australian Research Council.We are grateful to Professors M. Seetharama Gowda, Olvi Mangasarian, Jong-Shi Pang, and Steve Robinson for references. We are thankful to Professor Jim Burke for discussions on Theorem 2.1 and Counterexample 3.5. 相似文献
8.
称局部凸空间(E,(?)0)为WCM空间若对于任何弱于(?)0的局部凸拓扑(?),(E,(?))与(E,(?)0)具相同的弱紧圆凸集.本文研究了WCM空间的存在性及其与其他类型局部凸空间之间的关系,还给出了WCM空间的一种映照特征. 相似文献
9.
Jing Hui QIU 《数学学报(英文版)》2007,23(12):2295-2302
In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact. 相似文献
10.
N. V. Krylov 《Probability Theory and Related Fields》2002,123(4):521-552
A supermartingale characterization of sets of stochastic integrals is given along with its applications to control and diffusion
approximation. The characterization is convenient for passing to the limit. Under natural conditions it is proved that the
set of distributions of controlled diffusion processes is convex and compact.
Received: 16 July 2001 / Revised version: 1 November 2001 / Published online: 12 July 2002 相似文献
11.
Reduction of quasidifferentials and minimal representations 总被引:1,自引:0,他引:1
Some criterias for the non-minimality of pairs of compact convex sets of a real locally convex topological vector space are proved, based on a reduction technique via cutting planes and excision of compact convex subsets. Following an example of J. Grzybowski, we construct a class of equivalent minimal pairs of compact convex sets which are not connected by translations.Corresponding author. 相似文献
12.
Robert J. MacG. Dawson 《Journal of Geometry》2010,98(1-2):1-19
A set in a metric space is called a ?eby?ev set if it contains a unique “nearest neighbour” to each point of the space. In this paper we introduce the concept of a monotone arc of convex sets and show that compact monotone arcs have the ?eby?ev property in the hyperspace of compact strictly convex sets. In the hyperspace of compact convex sets only certain monotone arcs are ?eby?ev ; these are characterized. Results are also obtained for affine segments and for noncompact monotone arcs. 相似文献
13.
Jonathan M. Borwein Jon D. Vanderwerff 《Transactions of the American Mathematical Society》1996,348(4):1617-1631
We examine when a sequence of lsc convex functions on a Banach space converges uniformly on bounded sets (resp. compact sets) provided it converges Attouch-Wets (resp. Painlevé-Kuratowski). We also obtain related results for pointwise convergence and uniform convergence on weakly compact sets. Some known results concerning the convergence of sequences of linear functionals are shown to also hold for lsc convex functions. For example, a sequence of lsc convex functions converges uniformly on bounded sets to a continuous affine function provided that the convergence is uniform on weakly compact sets and the space does not contain an isomorphic copy of .
14.
Collectively compact sets of (linear) operators in Banach spaces have been studied and used by P. M. Anselone [2] and others in connection with integral operators. In this paper we show that a relevant part of the theory extends to bounded (in general nonlinear) operators in locally convex spaces. 相似文献
15.
This paper is a continuation of the author's first paper (Set-Valued Anal.
9 (2001), pp. 217–245), where the normed and partially ordered vector space of directed sets is constructed and the cone of all nonempty convex compact sets in R
n
is embedded. A visualization of directed sets and of differences of convex compact sets is presented and its geometrical components and properties are studied. The three components of the visualization are compared with other known differences of convex compact sets. 相似文献
16.
We prove that a collection of compact convex sets of bounded diameters in
that is unbounded in k independent directions has a k-flat transversal for k<d if and only if every d+1 of the sets have a k-transversal. This result generalizes a theorem of Hadwiger(–Danzer–Grünbaum–Klee) on line transversals for an unbounded family of compact convex sets. It is the first Helly-type theorem known for transversals of dimension between 1 and d−1. 相似文献
17.
Jean-Baptiste Hiriart-Urruty 《Journal of Global Optimization》2009,45(2):335-336
We present an open global minimization problem: it concerns the minimization of the volume among the compact convex sets in
\mathbbR3{\mathbb{R}^{3}} of a given constant thickness. 相似文献
18.
Jean-Paul Penot 《Proceedings of the American Mathematical Society》2003,131(8):2371-2377
We present fixed point theorems for a nonexpansive mapping from a closed convex subset of a uniformly convex Banach space into itself under some asymptotic contraction assumptions. They generalize results valid for bounded convex sets or asymptotically compact sets.
19.
Renxing Ni 《Journal of Mathematical Analysis and Applications》2006,316(2):642-651
The relationship between directional derivatives of generalized farthest functions and the existence of generalized farthest points in Banach spaces is investigated. It is proved that the generalized farthest function generated by a bounded closed set having a one-sided directional derivative equal to 1 or −1 implies the existence of generalized farthest points. New characterization theorems of (compact) locally uniformly convex sets are given. 相似文献