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Limiting subdifferentials of indefinite integrals

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
341
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2007.10.020
Keywords
  • Indefinite Integral
  • Fréchet Subdifferential
  • Limiting Subdifferential
  • Aumann Integral
Disciplines
  • Computer Science

Abstract

Abstract We compute the limiting subdifferential ∂ F ( x ¯ ) of the indefinite integral of the form F ( x ) = ∫ a x f ( t ) d t where f is an essentially bounded measurable function, or a function continuous on an interval containing x ¯ ∈ R (except for, possibly, x ¯ ), or a step-function which has a countable number of steps around x ¯ . The related problem of computing the Aumann integral of the limiting subdifferential mapping ∂ f ( ⋅ ) , where f is a Lipschitz real function defined on an open set U ⊂ R n , is also investigated.

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