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Effective properties in compact sets of Borel functions

  • Gabriel Debs (a1)

We prove that, if (fn)n∈ω is a sequence of continuous functions on some recursively presentable Polish space, such that any pointwise cluster point of (fn)n∈ω is a Borel function, then there exists a -subsequence of (fn)n∈ω which is pointwise convergent. This is an effective version of a well known result of Bourgain, Fremlin and Talagrand.

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1. J. Bourgain , D. H. Fremlin and M. Talagrand . Pointwise compact sets of Baire measurable functions. Amer. J. Math., 100 (1978), 845886.

3. H. P. Rosenthal . Pointwise compact subsets of first Baire class. Amer. J. Math., 99 (1977), 362378.

4. R. M. Solovay . Hyperarithmetical encodable sets. Trans. Amer. Math. Soc., 239 (1978), 99122.

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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