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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.Bourgain J., Fremlin D. H. and Talagrand M.. Pointwise compact sets of Baire measurable functions. Amer. J. Math., 100 (1978), 845886.
2.Moschovakis Y. N.. Descriptive Set Theory. Studies in Logic, vol. 100 (North-Holland, 1980).
3.Rosenthal H. P.. Pointwise compact subsets of first Baire class. Amer. J. Math., 99 (1977), 362378.
4.Solovay R. M.. 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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