The Lévy-Hinčin representation for random compact convex subsets which are infinitely divisible under Minkowski addition

1985 ◽  
Vol 70 (2) ◽  
pp. 271-287 ◽  
Author(s):  
Evarist Gine ◽  
Marjorie G. Hahn
Keyword(s):  
Compact Convex ◽  
Infinitely Divisible ◽  
Minkowski Addition ◽  
Convex Subsets

Random compact convex sets which are infinitely divisible with respect to Minkowski addition

1979 ◽  
Vol 11 (4) ◽  
pp. 834-850 ◽  
Author(s):  
Shigeru Mase
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Infinite Divisibility ◽  
Spectral Measures ◽  
Infinitely Divisible ◽  
Minkowski Addition ◽  
Closed Sets ◽  
Random Closed Sets ◽  
Canonical Representations ◽  
Laplace Transformations

Random closed sets (in Matheron's sense) which are a.s. compact convex and contain the origin are considered. The totality of such random closed sets are closed under the Minkowski addition and we can define the concept of infinite divisibility with respect to Minkowski addition of random compact convex sets. Using a generalized notion of Laplace transformations we get Lévy-type canonical representations of infinitely divisible random compact convex sets. Isotropic and stable cases are also considered. Finally we get several mean formulas of Minkowski functionals of infinitely divisible random compact convex sets in terms of their Lévy spectral measures.

Random compact convex sets which are infinitely divisible with respect to Minkowski addition

1979 ◽  
Vol 11 (04) ◽  
pp. 834-850 ◽  
Author(s):  
Shigeru Mase
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Infinite Divisibility ◽  
Spectral Measures ◽  
Infinitely Divisible ◽  
Minkowski Addition ◽  
Closed Sets ◽  
Random Closed Sets ◽  
Canonical Representations ◽  
Laplace Transformations

Random closed sets (in Matheron's sense) which are a.s. compact convex and contain the origin are considered. The totality of such random closed sets are closed under the Minkowski addition and we can define the concept of infinite divisibility with respect to Minkowski addition of random compact convex sets. Using a generalized notion of Laplace transformations we get Lévy-type canonical representations of infinitely divisible random compact convex sets. Isotropic and stable cases are also considered. Finally we get several mean formulas of Minkowski functionals of infinitely divisible random compact convex sets in terms of their Lévy spectral measures.

Completely stretched sets

1974 ◽  
Vol 75 (1) ◽  
pp. 37-43 ◽  
Author(s):  
J. N. Lillington
Keyword(s):  
Euclidean Plane ◽  
Compact Convex ◽  
Connected Sets ◽  
Image Position ◽  
Convex Subsets

Introduction. All the sets X considered in this paper will be compact convex subsets of the Euclidean plane R. We shall require the following definitions. For x, y, z ∈ R let L(x, y, x) denote the minimum of all the lengths of all connected sets containing x, y and z. Define the stretch of x with respect to X to beand the stretch of X to be

scholarly journals On compact convex subsets of $D[0,1]$

1981 ◽  
Vol 11 (4) ◽  
pp. 501-510 ◽  
Author(s):  
Peter Z. Daffer
Keyword(s):  
Compact Convex ◽  
Convex Subsets

scholarly journals New fixed point free nonexpansive maps on weakly compact, convex subsets of L1[0,1]

2007 ◽  
Vol 180 (3) ◽  
pp. 271-284 ◽  
Author(s):  
P. N. Dowling ◽  
C. J. Lennard ◽  
B. Turett
Keyword(s):  
Fixed Point ◽  
Compact Convex ◽  
Weakly Compact ◽  
Nonexpansive Maps ◽  
Convex Subsets

scholarly journals Distances between convex subsets of state spaces

1985 ◽  
Vol 32 (1) ◽  
pp. 109-117
Author(s):  
A.J. Ellis
Keyword(s):  
State Space ◽  
Hausdorff Space ◽  
Compact Convex ◽  
The State ◽  
Facial Structure ◽  
State Spaces ◽  
New Criteria ◽  
Uniformly Closed ◽  
Geometric Nature ◽  
Convex Subsets

Let L be a closed linear space of continuous real-valued functions, containing constants, on a compact Hausdorff space Ω. This paper gives some new criteria for a closed subset E of Ω to be an L-interpolation set, or more generally for L|E to be uniformly closed or simplicial, in terms of distances between certain compact convex subsets of the state space of L. These criteria involve the facial structure of the state space and hence are of a geometric nature. The results sharpen some standard results of Glicksberg.

The Fixed Point Property in c0

1998 ◽  
Vol 41 (4) ◽  
pp. 413-422 ◽  
Author(s):  
Enrique Llorens-Fuster ◽  
Brailey Sims
Keyword(s):  
Fixed Point ◽  
Convex Subset ◽  
Weak Topology ◽  
Compact Convex ◽  
Fixed Point Property ◽  
Nonempty Interior ◽  
Point Property ◽  
Nonempty Convex ◽  
Convex Subsets

AbstractA closed convex subset of c0 has the fixed point property (fpp) if every nonexpansive self mapping of it has a fixed point. All nonempty weak compact convex subsets of c0 are known to have the fpp. We show that closed convex subsets with a nonempty interior and nonempty convex subsets which are compact in a topology slightly coarser than the weak topology may fail to have the fpp.

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