In the book of real analysis by Prof. Stein on p.76, I am confused about the following:
Why is the set $E$ in $\mathbb{R}^2$ has measure zero and $E^y$ is noe measurable at $y=0$.
Can someone give me a more concrete example to show this?
2026-04-27 19:47:06.1777319226
$E$ measurable in $\mathbb{R}^2$ but $E^y$ not measurable for $y=0$
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In Chapter 1 they describe the construction of a non-measurable set in $\mathbb{R}$. The subset $E$ described in your screenshot is the same set, but viewed as a subset of $\mathbb{R}^2$. It has zero measure when viewed as a subset of $\mathbb{R}^2$, but the slice $E^y$ is the the same non-measurable set from Chapter 1.