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- funció matemàtica (ca)
- functions obtained from continuous functions by transfinite iteration of the operation of forming pointwise limits of sequences of functions (en)
- reelle Funktionen Mathematik (de)
- множества математических функций, определяемые согласно классификации, введённой французским математиком Рене-Луи Бэром (ru)
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- We present two proofs.
# This can be seen by noting that for any finite collection of rationals, the characteristic function for this set is Baire 1: namely the function converges identically to the characteristic function of , where is the finite collection of rationals. Since the rationals are countable, we can look at the pointwise limit of these things over , where is an enumeration of the rationals. It is not Baire-1 by the theorem mentioned above: the set of discontinuities is the entire interval .
# The Dirichlet function can be constructed as the double pointwise limit of a sequence of continuous functions, as follows:
:::
:: for integer j and k. (en)
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- Baire function (en)
- Bairesche Klasse (de)
- Fonction de Baire (fr)
- ベール関数 (ja)
- Классы Бэра (ru)
- Класи Бера (uk)
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