Show whether E is a Measurable Set

Let be a sequence of measurable sets in . Let be a subset of so that if and only if belongs to exactly 2 of the sets . Determine whether E is measurable. If it is, show it. If not, give a counterexample.

I suppose it is measurable? No? Can't think of any counterexample.

Thanks in advance.

Re: Show whether E is a Measurable Set

for any two positive integers consider the set . Such sets are measurable and is a union of such sets

Re: Show whether E is a Measurable Set

Quote:

Originally Posted by

**Markeur** Let

be a sequence of measurable sets in

. Let

be a subset of

so that

if and only if

belongs to exactly 2 of the sets

. Determine whether E is measurable. If it is, show it. If not, give a counterexample.

I suppose it is measurable? No? Can't think of any counterexample.

Thanks in advance.

In my opinion any question about "something" should start off with a definition of "something" and a demonstration that the definition is satis fied. So here is my little contribution as a matter of principle from http://en.wikipedia.org/wiki/Measure_(mathematics)

σ-algebra, meaning that unions, intersections and complements of sequences of measurable subsets are measurable.

Let *Σ* be a σ-algebra over a set *X*. A function *μ* from *Σ* to the extended real number line is called a **measure** if it satisfies the following properties:

http://upload.wikimedia.org/wikipedi...359301d7ec.png for all http://upload.wikimedia.org/wikipedi...0fce1e8199.png

http://upload.wikimedia.org/wikipedi...46cdd70cb1.png

http://upload.wikimedia.org/wikipedi...9076c0df86.png

I would find it interesting to see how this would be done in the case of the previous post.