Due Septembre 7
If are a closed and a compact disjoint sets, then .
If is closed, then it is measurable. Follow the next steps.
- Prove that it is sufficient to assume that E is compact, and thus
- Given , choose an open with Prove that we can write , where the are disjoint open intervals.
- If are disjoint open intervals, then
- For each N, .
- Conclude .
Find a sequence of measurable sets such that, for , .
For , let .
- If E is compact, then .
- The previous may fail is E is closed and unbounded, or bounded and open.