Tagged Questions
3
votes
1answer
43 views
Finite Partitions of the Unit Interval
Does the unit interval have a finite partition $P$ such that no element of $P$ contains an open interval? I would think that the answer is no, because each element of $P$ would have Lebesgue measure ...
1
vote
0answers
121 views
Jordan Measure, Semi-closed sets and Partitions
From earlier question here. Consider
$$\mu \left( (0,1) \cap \mathbb Q \right) = 0$$
where
$$(0,1) = (0,\frac{1}{3})\cup [\frac{1}{3}, \frac{2}{3}] \cup (\frac{2}{3}, 1)$$ so
$$ \mu ((0,1) \cap ...
2
votes
2answers
248 views
Jordan Measures, Open sets, Closed sets and Semi-closed sets
I cannot understand:
$$\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 ...
