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Γ-convergence in Metric Spaces

  • Gianni Dal Maso
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 8)

Abstract

In this chapter we study some properties of Γ-limits when X is metrizable, or, more generally, when X is completely regular. In particular we shall prove that an equi-coercive sequence of functions (F h ) Γ-converges to a function F if and only in
$$ \mathop{{\min }}\limits_{{x \in X}} \left( {F + G} \right)(x) = \mathop{{\lim }}\limits_{{h \to \infty }} \;\mathop{{\inf }}\limits_{{x \in X}} \;\left( {{F_h} + G} \right)(x) $$
for every non-negative continuous function G: XR (compare with Theorem 7.8).

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Gianni Dal Maso
    • 1
  1. 1.International School for Advanced Studies (SISSA)TriesteItaly

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