A function F:R2-->R is sup-measurable if Ff:R-->R given by Ff(x)=F(x,f(x)), x in R, is measurable for each measurable function f:R2-->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 similar result for the original measurable case is the subject of a work in prepartion by Roslanowski and Shelah.
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Last modified January 16, 2001.