# 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. - published version (14p)

Bib entry

@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}, doi = {10.1515/JAA.2000.159}, mrclass = {03E35 (26A15 26B40 54H05)}, mrnumber = {1805097}, mrreviewer = {Klaas Pieter Hart}, doi = {10.1515/JAA.2000.159}, note = {\href{https://arxiv.org/abs/math/9905147}{arXiv: math/9905147}}, arxiv_number = {math/9905147} }