### 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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