It might help to look at it this way:

Then use the measurability condition for the measurable set on

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- Sep 23rd 2009, 07:13 PM #1
## m(E_1 U E_2)+m(E_1 ^ E_2)=mE_1+mE_2

Hello everyone. I've been hitting my head against the chalk-board trying to figure this one out.

Suppose and are Lebesgue measurable. Then we want to show that:

.

Recall:

Also Recall: E is measurable means for any set .

Any help on this problem would be greatly appreciated!

- Sep 23rd 2009, 08:14 PM #2

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- Sep 24th 2009, 01:53 PM #3

- Sep 24th 2009, 06:12 PM #4
Thanks! This proof is fairly self-explanatory, although it is missing a critical piece, and I cannot find the lemma anywhere in any textbook, and I am having difficulty proving it.

Assume that and are measurable. w.t.s. .

Set and . Clearly, is measurable.

Now,

and;

Now, I'm having trouble with , this seems to be the last road block to tackle.

P.S.: A is any set for which m is defined. And, is a covering of A.

- Sep 24th 2009, 09:05 PM #5

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- Sep 25th 2009, 10:44 AM #6