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The measure under consideration is the Lebesgue measure.
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coudy
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Does every measurable set in the plane with positive Lebesgue measure contain a cartesian product of two measurable sets of the real line with positive Lebesgue measures?

Does every measurable set in the plane with positive measure contain a cartesian product of two measurable sets of the real line with positive measures?

Does every measurable set in the plane with positive Lebesgue measure contain a cartesian product of two measurable sets of the real line with positive Lebesgue measures?

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Sofia
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Plane measurable sets and measurable rectangle

Does every measurable set in the plane with positive measure contain a cartesian product of two measurable sets of the real line with positive measures?