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**kat-m****Member**- Registered: 2010-06-14
- Posts: 2

Let

and . Let for and . Then, showi dont get this at all. please help me

*Last edited by kat-m (2010-06-14 06:40:52)*

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

i dont get this at all.

Good. Because you shouldn't. delta is a subset of R^2, and I_n is a subset of R. The statement "d = \cap I_n" doesn't make sense.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**kat-m****Member**- Registered: 2010-06-14
- Posts: 2

Thats what i thought. so how do you show

is measurable if you suppose and are complete measure spaces, where is legesgue measure and is counting measure?Offline

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Think about dividing the square [0,1] x [0,1] into n^2 little blocks. Then you want to only include those little blocks which contain some piece of delta. Which are those going to be? Now do this as n goes to infinity by taking an intersection.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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