Recent content by frogs11

  1. F

    Measure Theory: Prove Set is Measurable Question

    Hey, still stuck on this one. Let me know if you need me to clarify anything. Thanks!
  2. F

    Measure Theory: Prove Set is Measurable Question

    ...Anyone out there?
  3. F

    Measure Theory: Prove Set is Measurable Question

    One way that I have looked to prove (a) is to use the lemma that: If E ⊂ Rd, then m∗(E) = inf m∗(O), where the infimum is taken over all open sets O containing E. To construct an open set O1 that encompasses E1 and such that m∗(E1) = inf m∗(O1). And likewise and open set that encompasses...
  4. F

    Measure Theory: Prove Set is Measurable Question

    Homework Statement The question is from Stein, "Analysis 2", Chapter 1, Problem 5: Suppose E is measurable with m(E) < ∞, and E = E1 ∪ E2, E1 ∩ E2 = ∅. Prove: a) If m(E) = m∗(E1) + m∗(E2), then E1 and E2 are measurable. b) In particular, if E ⊂ Q, where Q is a finite cube, then...