Approximation of Accumulation Points of Sequences of Continuous Functions on Polish Spaces by Subsequences
نویسنده
چکیده
It is known that accumulation points of a pointwise bounded sequence (f n) n of continuous functions on a Polish space are pointwise limits of subsequences if all accumulation points are Borel. Here we present a quantitative variant of this result: For 0 0 and any accumulation point f there is a subsequence (f nk) k with lim sup k jf(x) ? f nk (x)j 0 for all x provided that every accumulation point is 0 =2-close to a Borel function. We will indicate the r^ ole of Martin's axiom if one wants to decide whether there is a best possible 0 with the above property.
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