Geodesic
Some generalizations of results of Carathéodory and Miller
Acta Universitatis Lodziensis. Folia Mathematica, Tome 04 (1991).

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This paper concerns measurable functions. It is shown that in the Miller theorem from [2] the assumption about the set J can be weakened. Moreover, it turns out that the carrying over of the Caratheodory theorem from [1] to the case of functions and sets having the Baire property is impossible. 
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     title = {Some generalizations of results of {Carath\'eodory} and {Miller}},
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Poreda, Wiesława. Some generalizations of results of Carathéodory and Miller. Acta Universitatis Lodziensis. Folia Mathematica, Tome 04 (1991). http://geodesic.mathdoc.fr/item/AULFM_1991_04_a15/