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Choquet Integrals

  • David R. Adams
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

One of the new development in the Theory of Morrey spaces - as far as this author is concerned - is the use of Hausdorff capacity and its corresponding Choquet Integral \((\int f\;d\,\Lambda ^{d})\) in the development of the predual to \(L^{p,\lambda }(\mathbb{R}^{n})\). This we do in the next chapter once we have thoroughly discussed all the tools that are needed to understand and apply these “non-linear” integrals. And it is because \(\Lambda ^{d}\) is not a measure (i.e., not countable additive on disjoint sets) that we must carefully define and expose all of the relevant properties of such an integral.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • David R. Adams
    • 1
  1. 1.Department of MathematicsUniversity of KentuckyLexingtonUSA

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