We prove that for every Borel ideal, the ideal limits of sequences of continuous functions on a Polish space are of Baire class one if and only if the ideal does not contain a copy of Fin × Fin. In particular, this is true for ideals. In the proof we use Borel determinacy for a game introduced by C. Laflamme.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-3,
author = {Mikl\'os Laczkovich and Ireneusz Rec\l aw},
title = {Ideal limits of sequences of continuous functions},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {39-46},
zbl = {1172.03025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-3}
}
Miklós Laczkovich; Ireneusz Recław. Ideal limits of sequences of continuous functions. Fundamenta Mathematicae, Tome 205 (2009) pp. 39-46. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-3/