It might help to look at it this way:
Then use the measurability condition for the measurable set on
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:
Also Recall: E is measurable means for any set .
Any help on this problem would be greatly appreciated!
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, 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.