Description: The Lebesgue outer measure of a set is an extended real. (Contributed by Glauco Siliprandi, 11-Oct-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ovnxrcl.1 | |- ( ph -> X e. Fin ) |
|
ovnxrcl.2 | |- ( ph -> A C_ ( RR ^m X ) ) |
||
Assertion | ovnxrcl | |- ( ph -> ( ( voln* ` X ) ` A ) e. RR* ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ovnxrcl.1 | |- ( ph -> X e. Fin ) |
|
2 | ovnxrcl.2 | |- ( ph -> A C_ ( RR ^m X ) ) |
|
3 | iccssxr | |- ( 0 [,] +oo ) C_ RR* |
|
4 | 1 2 | ovncl | |- ( ph -> ( ( voln* ` X ) ` A ) e. ( 0 [,] +oo ) ) |
5 | 3 4 | sselid | |- ( ph -> ( ( voln* ` X ) ` A ) e. RR* ) |