Measurable rectangles
Logic
2008-02-03 v1
Abstract
We give an example of a measurable set of reals E such that the set E'={(x,y): x+y in E} is not in the sigma-algebra generated by the rectangles with measurable sides. We also prove a stronger result that there exists an analytic set E such that E' is not in the sigma-algebra generated by rectangles whose horizontal side is measurable and vertical side is arbitrary. The same results are true when measurable is replaced with property of Baire.
Cite
@article{arxiv.math/9211206,
title = {Measurable rectangles},
author = {Arnold W. Miller},
journal= {arXiv preprint arXiv:math/9211206},
year = {2008}
}