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Best approximation properties in spaces of measurable functions

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  • Maciej Ciesielski
  • Grzegorz Lewicki

Abstract

We research proximinality of μ†sequentially compact sets and μ†compact sets in measurable function spaces. Next we show a correspondence between the Kadec–Klee property for convergence in measure and μ†compactness of the sets in Banach function spaces. Also the property S is investigated in Fréchet spaces and employed to provide the Kadec–Klee property for local convergence in measure. We discuss complete criteria for continuity of metric projection in Fréchet spaces with respect to the Hausdorff distance. Finally, we present the necessary and sufficient condition for continuous metric selection onto a one†dimensional subspace in sequence Lorentz spaces d(w,1).

Suggested Citation

  • Maciej Ciesielski & Grzegorz Lewicki, 2018. "Best approximation properties in spaces of measurable functions," Mathematische Nachrichten, Wiley Blackwell, vol. 291(4), pages 610-631, March.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:4:p:610-631
    DOI: 10.1002/mana.201600485
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