The first part of Cavalieri's principle (in measure theory) states if $E$ is measurable, then almost every slice $E_x$ of $E$ is measurable.
Here, it uses "almost every", so what is an example where not all slices of E is measurable?
Thanks!
2026-04-08 17:36:59.1775669819
Cavalieri's Principle in measure theory
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Couldn't you take a set of the form $\{0\} \times A$, where $A$ is non-measurable? This is measurable of measure zero, being a subset of the the measure zero set $\{0\} \times \mathbb{R}$.