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The paper describes results of Polish mathematicians of XX century concerning the Baire classification of functions and Borel classification of sets. As usual, numerous theorems came from Wacław Sierpiński, remaining are due to Kazimierz Kuratowski, Stefan Banach, Stefan Kempisty, Edward Szpilrajn (Marczewski), Andrzej Alexiewicz, Władysław Orlicz, Adolf Lindenbaum, Roman Sikorski, Ryszard Engelking,...
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