We determine the Borel class of the image of a Polish space under a Borel measurable function of classɦwhich maps open sets in the Polish space to Borel sets of additive class£ in the range, under a mild restriction on the inverse images of singleton sets. Our computation is based on a selection theorem proved in this article
Levi, S., Maitra, A. (1984). Borel measurable images of Polish spaces. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 92(1), 98-102 [10.1090/S0002-9939-1984-0749900-4].
Borel measurable images of Polish spaces
LEVI, SANDRO;
1984
Abstract
We determine the Borel class of the image of a Polish space under a Borel measurable function of classɦwhich maps open sets in the Polish space to Borel sets of additive class£ in the range, under a mild restriction on the inverse images of singleton sets. Our computation is based on a selection theorem proved in this article
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