Suppose E and F are measurable sets of finite measures and E is contained in G contained in F. Prove G is measurable. I tried using the equivalence relation of measurable sets, but I see no reason why I should let epsylom
2026-03-25 18:59:58.1774465198
Measurable sets
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This is not true. For example, let $E=\emptyset$, $F=[0,1]$. Then this would imply that every subset of $[0,1]$ is measurable, which is very false.
I think that this question is missing two conditions, namely that $\mu(E) = \mu(F)$, and $\mu$ is a complete measure (it is possible that you are specifically using the Lebesgue measure, but you didn't say so). If you have these conditions the result is true. A hint for proving this is to consider the set $F\setminus E$.