Description: The domain of the Lebesgue outer measure is the power set of the n-dimensional Real numbers. Step (a)(i) of the proof of Proposition 115D (a) of Fremlin1 p. 30. (Contributed by Glauco Siliprandi, 24-Dec-2020)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | dmovn.1 | |- ( ph -> X e. Fin ) |
|
| Assertion | dmovn | |- ( ph -> dom ( voln* ` X ) = ~P ( RR ^m X ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dmovn.1 | |- ( ph -> X e. Fin ) |
|
| 2 | 1 | ovnf | |- ( ph -> ( voln* ` X ) : ~P ( RR ^m X ) --> ( 0 [,] +oo ) ) |
| 3 | 2 | fdmd | |- ( ph -> dom ( voln* ` X ) = ~P ( RR ^m X ) ) |