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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