measure theory - What does measurable mean intuitively? - Mathematics . . . Now the measurable ones form a $\sigma$-algebra, which in retrospect justifies calling them measurable If we now restrict the outer measure to the measurable sets, we get an actual measure which captures the idea we used to define the outer measure, and behaves nicely as well
Proving every compact set on $\\mathbb{R}$ is measurable So we can show that every open interval $(a_n,b_n)$ is measurable A set is measurable on the real line if it can be approximated with respect to the Lebesgue $\text{outer}$ measure by open supersets In other words: Let $\epsilon>0$
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