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Download pdf Humanizing : the drug industry. In the early years of the Third Millennium, six billion people lived on the planet Earth. They lived different lives. Some lived in the white, northern climes. Some lived in the black, southern climes. Some lived in the eastern, Oriental climes.Q:
$\mu (\bar{A}) = \mu(\mathbb{R})$ implies $\mu(A) = \mu(B)$?
If $X$ is a measure space and $A \subset B \subset X$ ($B$ is closed) are measurable sets then $\mu(\mathbb{R}) = \mu(\bar{A})$ and $\mu(A) = \mu(\mathbb{R})$. The final equality also follows from the fact that the set $\bar{A}$ is a closed set that contains the open set $X \setminus A$.
My question is about the first equality. If $B \subset \mathbb{R}$ and $A = \mathbb{R} \setminus B$ (or equivalently $A = \mathbb{R} \setminus \overline{B}$), then we have that $\mu(A) = \mu(\mathbb{R})$. Is the assumption that $B$ is a closed set necessary in the above observation?
A:
Let $B=(-2,2)$ and let $A =\mathbb R \setminus B = (0,\infty)$.
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Howey wrote in hindsight that Sand might have been the third installment in a trilogy, a theory given credence when he announced in late 2012 that he was.
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