Let be an algebra,
and let be the collection of countable union of sets in .
Let be the collection of countable intersection of sets in .
Let be a premeasure on .
Let be outer measure with [tex] \mu* \mid _
Prove that if , then is -measurable iff with and
Note:
Proof so far.
First, I assume that with and
So I have
Implies that
Implies that
But what I need is , then of course, all I have to show is that since the other inequality follows from the property of outer measure.
Any hints? Thank you.