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    $\begingroup$ Although the question was already answered, you may be interested in this: There is an excellent short little book by Oxtoby, "Measure and Category", where all these "classical" relations between both notions are discussed; you may want to take a look. There are deeper relations and differences, but you need set theory to understand them; a good book to look at is "Set theory: On the structure of the real line", by Bartoszynski and Judah. $\endgroup$
    – Andrés E. Caicedo
    Commented Oct 25, 2010 at 5:48
  • $\begingroup$ Interesting spelling ... my dictionary says (non-math context) US spelling meager and UK spelling meagre. I suppose this goes along with theater/theatre and similar. $\endgroup$
    – Gerald Edgar
    Commented Oct 25, 2010 at 15:16
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    $\begingroup$ I went with the Wikipedia spelling since that's what I was linking to, but I would normally spell it meager. $\endgroup$
    – Anton Geraschenko
    Commented Oct 25, 2010 at 17:56
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    $\begingroup$ I see that Wikipedia page has neighbourhood so other UK spellings are not unexpected. But shouldn't it then be Wikipaedia? $\endgroup$
    – Gerald Edgar
    Commented Oct 25, 2010 at 23:31
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    $\begingroup$ Is there a measure 0 set which is nowhere meager? Can such a set be Borel? $\endgroup$
    – Marcel Besixdouze
    Commented Jul 31, 2014 at 8:06