14. Let A ⊆ ℝ, then which of the following is false.
1 Mark
A. Every subset of A is Lebesgue measurable implies that m(A) = 0.
B. Every Lebesgue measurable set is a Borel set.
C. If A is measurable and m(A) = 0, then there exists a subset of A which is not Lebesgue measurable.
D. There exists a non-Lebesgue measurable subset of [0, 1].
15. If μ is a positive measure and μ* is the outer measure induced by μ, then for any set E ⊆ ℝ, we have μ*(E) = inf{μ(U) : E ⊆ U, U is open}.