A Characterization of Epi-Convergence in Terms of Convergence of Level Sets
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Publication:4031456
DOI10.2307/2159443zbMath0769.49011OpenAlexW4233163261MaRDI QIDQ4031456
Roger J.-B. Wets, Gerald A. Beer, R. Tyrrell Rockafellar
Publication date: 1 April 1993
Full work available at URL: https://doi.org/10.2307/2159443
level setsseparable metrizable spaceepiconvergenceweakly lower semicontinuous functionsPK-limits of sets
Hyperspaces in general topology (54B20) Function spaces in general topology (54C35) Methods involving semicontinuity and convergence; relaxation (49J45)
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Cites Work
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- Convergence of best approximations in a smooth Banach space
- On convergence of convex sets and relative Chebyshev centers
- Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions
- The topology of the \(\rho\)-Hausdorff distance
- On the relations between two types of convergence for convex functions
- Convergence of convex sets and of solutions of variational inequalities
- On the continuity of the Young-Fenchel transform
- A Hausdorff Topology for the Closed Subsets of a Locally Compact Non-Hausdorff Space
- Metric spaces with nice closed balls and distance functions for closed sets
- Stopping Times and Γ-Convergence
- On Mosco convergence of convex sets
- Mosco Convergence and the Kadec Property
- Preservation of Convergence of Convex Sets and Functions in Finite Dimensions
- The Cosmic Hausdorff Topology, the Bounded Hausdorff Topology and Continuity of Polarity
- Quantitative Stability of Variational Systems: I. The Epigraphical Distance
- Mosco Convergence and Reflexivity
- Convex Optimization and the Epi-Distance Topology
- Conjugate Convex Functions and the Epi-Distance Topology
- Minima of quasi-convex functions
- Operations on convergent families of sets and functions
- Set-valued analysis