Theorem dmovnsal

Description: The domain of the Lebesgue measure is a sigma-algebra. (Contributed by Glauco Siliprandi, 24-Dec-2020)

	Ref	Expression
Hypotheses	dmovnsal.x	|- ( ph -> X e. Fin )
	dmovnsal.s	|- S = dom ( voln ` X )
Assertion	dmovnsal	|- ( ph -> S e. SAlg )

Proof

Step	Hyp	Ref	Expression
1		dmovnsal.x	|- ( ph -> X e. Fin )
2		dmovnsal.s	|- S = dom ( voln ` X )
3	1	vonmea	|- ( ph -> ( voln ` X ) e. Meas )
4	3 2	dmmeasal	|- ( ph -> S e. SAlg )