I am reading Measure and Category of Oxtoby. I have a question about Theorem 5.4 added below. I think I understand the construction of Bernstein sets, and also the main line of the Proof. My question is mush more basic I think:
Suppose that every measurable subset of either $B$ or $B'$ is a Nullset, and any subset of $B$ or $B'$ that has the property of Baire is of first category. Why, Does it implies that $B$ is non-measurable?
Am I missing something obvious? Thank you for your help!! Shir
I read this great book long time ago! Suppose that $B$ is measurable then its measure must be zero (since every measurable subset of $B$ is a nullset) and similarly the measure of $B'$ must also be zero which implies that $\Bbb{R}$ is a nullset. I am right ?