Re: sandwich measurable set

How do you know that ? You just stated what you need to prove, but did not prove it.

You need to show that for all and for all measurable sets , . So, you need to come up with a way of rewriting using the terms you know something about: .

Re: sandwich measurable set

I tried the way u provided, but i cannot get anything relatives to m(C\B)< ε . Could you tell me the proof in details???

Re: sandwich measurable set

Since and , you can conclude, . But, , so . Since are measurable, use the properties of a -algebra to show that are both measurable. Hence .

To recap, we have

This is because , so and since is measurable, .

So, finally, we have .