On Mar 23, 11:01 pm, quasi <qu...@null.set> wrote: > William Elliot wrote: > >Question: Is there a dense D, subset of R with > >empty interior and measure D /\ [0,1] = 1/2? > > Yes. > > Let > > A = (0,1/2)\Q > > B = Q\A > > D = A U B
Then B = Q\A = Q, and D = A U Q = (0,1/2) U Q has nonempty interior.
Of course you meant to say B = Q\(0,1/2), so that A is the symmetric difference of (0,1/2) and Q.