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fsblajinha
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Is $q_ {1} q_ {2}, ...,$ an enumeration of the rational $[0,1]$. For every $\epsilon> 0$, let $\displaystyle{A _ {\epsilon}: = [0,1]-\bigcup_ {n \geq 1} I_{n}}$, where $I_{n}:= [q_{n} - \frac {\epsilon}{2^{n+1}} , q_{n}\frac{\epsilon}{2^{n + 1}}]\cap [0,1]$.
Show that:
1 - $A _ {\epsilon}$ is measurable, non-empty and empty inside;
2 - $\lambda^{*}(B)=1$, where $\displaystyle B:=\bigcup_{k\geq 1}{A_\frac{1}{k}}$
Show that:
1 - $A _ {\epsilon}$ is measurable, non-empty and empty inside;
2 - $\lambda^{*}(B)=1$, where $\displaystyle B:=\bigcup_{k\geq 1}{A_\frac{1}{k}}$
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