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I have just checked the definition of a measure in the MIT's measure theory pdf for the first lecture.

And their $(\sigma_1)$ condition is that $X \in \mathcal{M}$. Where $X$ is a space and $\mathcal M$ is a measure. And I cannot quite understand how space can be an element of measure. I thought that measure is just a function that maps subsets of $X$ into $\mathbb{R}$.

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    $\begingroup$ $\mathcal M$ is not a measure. It is a $\sigma$-algebra. $\endgroup$
    – user228113
    Nov 20, 2016 at 21:42
  • $\begingroup$ oh dear. thanks. $\endgroup$
    – Naz
    Nov 20, 2016 at 21:42

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$\mathcal M$ is not a measure. It is a $\sigma$-algebra.

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