scholarly journals Models for growth of heterogeneous sandpiles via Mosco convergence

2012 ◽  
Vol 78 (1-2) ◽  
pp. 11-36 ◽  
Author(s):  
M. Bocea ◽  
M. Mihăilescu ◽  
M. Pérez-Llanos ◽  
J.D. Rossi
Keyword(s):  
Mosco Convergence

scholarly journals Convergence theorems for Banach space valued integrable multifunctions

1987 ◽  
Vol 10 (3) ◽  
pp. 433-442 ◽  
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Convergent Sequence ◽  
Mosco Convergence ◽  
Convergence Theorems ◽  
Aumann Integral ◽  
Convergence Results ◽  
Measurable Multifunctions ◽  
Dominated Convergence ◽  
Convergence Of Sets

In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spacesLXP(Ω) (1≤p≤∞). Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.

scholarly journals Properties of the trajectories of set-valued integrals in banach spaces

1990 ◽  
Vol 41 (2) ◽  
pp. 271-281
Author(s):  
Nikolaos S. Papageorgiou
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Separable Banach Space ◽  
Hausdorff Metric ◽  
Density Theorem ◽  
Mosco Convergence ◽  
Convexity Theorem ◽  
Convergence Theorems ◽  
Convergence Of Sets ◽  
Differentiability Properties

Let F: T → 2x \ {} be a closed-valued multifunction into a separable Banach space X. We define the sets and We prove various convergence theorems for those two sets using the Hausdorff metric and the Kuratowski-Mosco convergence of sets. Then we prove a density theorem of CF and a corresponding convexity theorem for F(·). Finally we study the “differentiability” properties of K(·). Our work extends and improves earlier ones by Artstein, Bridgland, Hermes and Papageorgiou.

scholarly journals On Mosco convergence of convex sets

1988 ◽  
Vol 38 (2) ◽  
pp. 239-253 ◽  
Author(s):  
Gerald Beer
Keyword(s):  
Convex Sets ◽  
Hausdorff Metric ◽  
Mosco Convergence ◽  
Natural Topology ◽  
Weakly Compact ◽  
Reflexive Space ◽  
Convergence Of Sequences ◽  
Metric Topology ◽  
Hausdorff Metric Topology

We present a natural topology compatible with the Mosco convergence of sequences of closed convex sets in a reflexive space, and characterise the topology in terms of the continuity of the distance between convex sets and fixed weakly compact ones. When the space is separable, the topology is Polish. As an application, we show that in this context, most closed convex sets are almost Chebyshev, a result that fails for the stronger Hausdorff metric topology.

scholarly journals Mosco convergence and reflexivity

1990 ◽  
Vol 109 (2) ◽  
pp. 427-427 ◽  
Author(s):  
Gerald Beer ◽  
Jonathan M. Borwein
Keyword(s):  
Mosco Convergence
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