I am told that by means of continued fractions, Lusin or somebody else, has constructed examples of Lebesgue measurable sets which are not Borel measurable. Please, if you know a reference help me.
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$\begingroup$ MathOverflow is for research-level questions only, see the FAQ: mathoverflow.net/faq#whatnot. Here is a thread on Math Stack Exchange where this topic is addressed: math.stackexchange.com/q/141017/264 $\endgroup$– Zev ChonolesCommented Jun 13, 2012 at 14:14
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$\begingroup$ @jorge: Google search gives lot of good results. Here is one which I liked: unapologetic.wordpress.com/2010/04/24/… $\endgroup$– C.S.Commented Jun 13, 2012 at 15:09
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1$\begingroup$ @Chandra: But that is not what he is asking for... $\endgroup$– Gerald EdgarCommented Jun 13, 2012 at 15:38
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$\begingroup$ There is an argument based on cardinality that shows that such sets exist. If one says ONLY that because of cardinalities such a set exists, that appears non-constructive. But I suspect by looking at the arguments that show that the cardinalities of such-and-such sets are thus-and-so, one may be able to come closer to constructing an example. But this seems unlikely to qualify as "research-level" math. $\endgroup$– Michael HardyCommented Oct 3 at 16:55
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