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espanolEn este articulo se presentan apartes de la discusion sobre el problema de existencia de funciones de cada una de las clases de Baire. Primero se plantea el problema historico, introduciendo cuatro categorias existenciales y luego se muestra la posicion del matematico ruso Nikolai Luzin en terminos de la teoria de la tematizacion. EnglishThis paper presents excerpts of the discussion about the problem of existence for functions in each one of Baire’ s classes. First, it sets up the historical problem, introducing four existential categories, and then it shows Luzin’ s position and reframes it in terms of Cavailles and Gardies’ theory of thematization. MSC2010: 00A30, 26A21, 03E15

Nikolai Luzin and the problem of existence in mathematics