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Mar 20, 2015 at 0:24 vote accept Alexander Pruss
Mar 20, 2015 at 0:14 comment added Alexander Pruss Thanks! The existence of a set $S$ with the requisite properties (well, or the equivalent claim on the square) also follows from Sierpinski's 1938 partition of the square into perfect sets such that any choice of one element of each of the perfect sets gives a set with full outer measure: eudml.org/doc/213031
Mar 19, 2015 at 21:36 history edited Eric Wofsey CC BY-SA 3.0
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Mar 19, 2015 at 21:25 comment added Fan Zheng But does "more than $c$" imply "$2^c$"?
Mar 19, 2015 at 21:01 history answered Eric Wofsey CC BY-SA 3.0