Sh:695

• Ciesielski, K. C., & Shelah, S. (2000). Category analogue of sup-measurability problem. J. Appl. Anal., 6(2), 159–172. arXiv: math/9905147 DOI: 10.1515/JAA.2000.159 MR: 1805097
• Abstract:
  A function F\colon{\mathbb R}^2\to{\mathbb R} is sup-measurable if F_f\colon{\mathbb R}\to{\mathbb R} given by F_f(x)=F(x,f(x)), x\in{\mathbb R}, is measurable for each measurable function f\colon{\mathbb R}\to{\mathbb 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.
• Version 2000-04-11_11 (17p) published version (14p)

@article{Sh:695,
 author = {Ciesielski, Krzysztof Chris and Shelah, Saharon},
 title = {{Category analogue of sup-measurability problem}},
 journal = {J. Appl. Anal.},
 fjournal = {Journal of Applied Analysis},
 volume = {6},
 number = {2},
 year = {2000},
 pages = {159--172},
 issn = {1425-6908},
 mrnumber = {1805097},
 mrclass = {03E35 (26A15 26B40 54H05)},
 doi = {10.1515/JAA.2000.159},
 note = {\href{https://arxiv.org/abs/math/9905147}{arXiv: math/9905147}},
 arxiv_number = {math/9905147}
}