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Abstract. We first prove that given any analytic filter F on ω the set of all functions f on 2 ω which can be represented as the pointwise limit relative to F of some sequence (fn)n∈ω of continuous functions (f = limF fn), is exactly the set of all Borel functions of class ξ for some countable ordinal ξ that we call the rank of F. We discuss several structural properties of this rank. For example, we prove that any free Π 0 4 filter is of rank 1.

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