What can you say about union of two non measurable set. They are measurable or not? Is it necessarily true?Thinking about α-cantor set I wonder if the complement of a non measurable set is a non measurable set that does the job.
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This is same question of mine.But someguys put an hold on that question. – Sayantan Koley Jan 21 '15 at 13:28
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See http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox – Janko Bracic Jan 21 '15 at 13:29
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http://math.stackexchange.com/questions/549987/countable-disjoint-union-of-non-measurable-sets – Clement C. Jan 21 '15 at 13:35
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If you believe that a non-measurable subset $A$ of $[0,1]$ exists then $A':=[0,1]\setminus A$ will be nonmeasurable as well, but the union $A\cup A'=[0,1]$ is measurable.
Christian Blatter
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Such non-measurable subset $A$ of $[0, 1]$always exists due to Vitali's theorem. – Cloud Walker Mar 27 '24 at 04:54