I cannot understand:
$\bar{\mu} ( \{Q \cap (0,1) \} ) = 1$
and (cannot understand this one particularly)
$\underline{\mu} ( \{Q \cap (0,1) \} ) = 0$
where $Q$ is rational numbers, why? I know that the measure for closed set $\mu ([0,1]) = 1$ so I am puzzled with the open set solution. Is $\underline{\mu} ( (0,1) ) = 0$ also? How is the measure with open sets in general?
So far the main question, history contains some helper questions but I think this is the lion part of it what I cannot understand. More about Jordan measure here.
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