Measurable rectangles

Arnold W. Miller

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arXiv · math/9211206

Measurable rectangles

Arnold W. Miller

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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.

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BibTeX RIS

Arnold W. Miller. 1992-11-25. Measurable rectangles. https://arxiv.org/abs/math/9211206

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