Title: Measurable Rectangles
Author: Arnold W. Miller
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.