Thread: 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.

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

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:

• Non-negativity:

for all

• Countable additivity (or σ-additivity): For all countable collections of pairwise disjoint sets in Σ:

• Null empty set:

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