Recent content by ntsivanidis

Homework Statement If E has finite measure and \epsilon>0, then E is the disjoint union of a finite number of measurable sets, each of which has measure at most \epsilon. Homework Equations The Attempt at a Solution I proceeded by showing that by definition of measure, there is a...

Thanks! Along what lines should I proceed? It's very shaky from that point onwards and I'm stumped for something more concrete. If you could describe a sketch, that would be great. Cheers

Hey guys, below is a small question from introductory measure theory. Maybe be completely wrong on this, so if you could point me in the right direction I'd really appreciate it. Claim: Let B=\mathbb{Q} \cap [0,1] and \{I_k\}_{k=1}^n be a finite open cover for B. Then \sum_{k=1}^n m^*(I_k)...