Category analogue of sup-measurability problem

by Ciesielski and Shelah. [CiSh:695]
J Applied Analysis, 2000
A function F : R^2-> R is sup-measurable if F_f : R-> R given by F_f(x)=F(x,f(x)), x in R, is measurable for each measurable function f : R-> R . It is known that under different set theoretical assumptions, including CH, there are sup-measurable non-measurable functions, as well as their category analog. In this paper we will show that the existence of category analog of sup-measurable non-measurable functions is independent of ZFC. A problem whether the similar is true for the original measurable case remains open.

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