Research Article

Effective properties in compact sets of Borel functions

Gabriel Debsa1

a1 Equipe d'Analyse, Université Paris VI, 4, Place Jussieu, 75252—Paris cedex 05, France.


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

(Received July 02 1986)

Key Words:

  • 04A15: SET THEORY; Descriptive set theory; Borel classifications.