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$\begingroup$ This is really ideal, expressing $[0,1]$ as a union of a meager set and a measure 0 set. That kills two birds with one stone. $\endgroup$
– Greg Kuperberg
Commented Oct 25, 2010 at 12:39
1

$\begingroup$ @Greg Kuperberg: well, as long as you have a co-meager set of measure 0, such as in the classical example from Oxtoby's book, then you have that. What's neat about Andreas Blass' example, though, is that it is very intuitive that it should have measure 0 and be comeager. $\endgroup$
– Bjørn Kjos-Hanssen
Commented Oct 25, 2010 at 18:33
4

$\begingroup$ So, the set of normal numbers is meagre and has full Lebesgue measure. $\endgroup$
– George Lowther
Commented Oct 25, 2010 at 23:25

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