Set-Valued Analysis

, Volume 1, Issue 4, pp 355–363 | Cite as

Convergence of decreasing sequences of convex sets in nonreflexive Banach spaces

  • Jonathan M. Borwein
  • Adrian S. Lewis


We consider nested sequences of linear or convex closed sets of the form arising in estimation and other inverse problems. We show that such sequences may fail to converge in any of the recently studied set convergences other than Mosco convergence. We also provide a positive result concerning the epislice convergence of related sequences of functions.

Mathematics Subject Classifications (1991)

Primary: 49A55, 90C25 secondary: 65K05, 49B27 

Key words

Set convergence Mosco convergence slice convergence Wijsman convergence Painlevé-Kuratowski convergence moment problems inverse problems nonreflexive spaces 


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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Jonathan M. Borwein
    • 1
  • Adrian S. Lewis
    • 2
  1. 1.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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