Theorem meaxrcl

Description: The measure of a set is an extended real. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Hypotheses	meaxrcl.1	|- ( ph -> M e. Meas )
	meaxrcl.2	|- S = dom M
	meaxrcl.3	|- ( ph -> A e. S )
Assertion	meaxrcl	|- ( ph -> ( M ` A ) e. RR* )

Proof

Step	Hyp	Ref	Expression
1		meaxrcl.1	|- ( ph -> M e. Meas )
2		meaxrcl.2	|- S = dom M
3		meaxrcl.3	|- ( ph -> A e. S )
4		iccssxr	|- ( 0 [,] +oo ) C_ RR*
5	1 2 3	meacl	|- ( ph -> ( M ` A ) e. ( 0 [,] +oo ) )
6	4 5	sseldi	|- ( ph -> ( M ` A ) e. RR* )