Hi all,

I'm having trouble with this problem. Hint given is to show thatGiven a set E; for each open, bounded interval (a,b):

b-a = m*((a,b)∩E) + m*((a,b)~E)

implies E is (Lebesgue) measurable.

(we're working with the real line here, so E is a subset of R)A = { E: b-a = m*((a,b)∩E) + m*((a,b)~E) }is a sigma algebra.

I understand the hint logic - if A is a sigma algebra then the sets in A are measurable sets so E must be measurable.

I know that all open, bounded intervals are measurable.

I know the three requirements for a collection of sets to be a sigma algebra.

I don't know how to connect the dots though.

Where do I start? Thanks