Abstract
We show that every mapping of the first functional Lebesgue class that acts from a topological space into a separable metrizable space that is linearly connected and locally linearly connected belongs to the first Baire class. We prove that the uniform limit of functions of the first Baire class ƒ n: X → Y belongs to the first Baire class if X is a topological space and Y is a metric space that is linearly connected and locally linearly connected.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 4, pp. 568–572, April, 2006.
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Karlova, O.O., Mykhailyuk, V.V. Functions of the first Baire class with values in metrizable spaces. Ukr Math J 58, 640–644 (2006). https://doi.org/10.1007/s11253-006-0089-2
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DOI: https://doi.org/10.1007/s11253-006-0089-2