Is the sum of two negligible sets always a negligible set?












0












$begingroup$


Let $E$ and $F$ be two negligible sets, is the following sum always a negligible set?



$E + F = {x + y : x ∈
E, y ∈ F}$



I tend to say no but I can't find any counter exemple






real-analysis measure-theory







share|cite|improve this question









$endgroup$

















    0












    $begingroup$


    Let $E$ and $F$ be two negligible sets, is the following sum always a negligible set?



    $E + F = {x + y : x ∈
    E, y ∈ F}$



    I tend to say no but I can't find any counter exemple






    real-analysis measure-theory







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      Let $E$ and $F$ be two negligible sets, is the following sum always a negligible set?



      $E + F = {x + y : x ∈
      E, y ∈ F}$



      I tend to say no but I can't find any counter exemple






      real-analysis measure-theory







      share|cite|improve this question









      $endgroup$




      Let $E$ and $F$ be two negligible sets, is the following sum always a negligible set?



      $E + F = {x + y : x ∈
      E, y ∈ F}$



      I tend to say no but I can't find any counter exemple






      real-analysis measure-theory




      real-analysis measure-theory






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 8 at 15:36









      Jonathan BaramJonathan Baram

      140113




      140113






















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          $begingroup$

          In general no. For instance, if $C$ is the Cantor set, then $C+C=[0,2]$.






          share|cite|improve this answer









          $endgroup$









          • 2




            $begingroup$
            Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
            $endgroup$
            – Jonathan Baram
            Jan 8 at 15:43











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          1 Answer
          1






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          active

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          active

          oldest

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          1












          $begingroup$

          In general no. For instance, if $C$ is the Cantor set, then $C+C=[0,2]$.






          share|cite|improve this answer









          $endgroup$









          • 2




            $begingroup$
            Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
            $endgroup$
            – Jonathan Baram
            Jan 8 at 15:43
















          1












          $begingroup$

          In general no. For instance, if $C$ is the Cantor set, then $C+C=[0,2]$.






          share|cite|improve this answer









          $endgroup$









          • 2




            $begingroup$
            Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
            $endgroup$
            – Jonathan Baram
            Jan 8 at 15:43














          1












          1








          1





          $begingroup$

          In general no. For instance, if $C$ is the Cantor set, then $C+C=[0,2]$.






          share|cite|improve this answer









          $endgroup$



          In general no. For instance, if $C$ is the Cantor set, then $C+C=[0,2]$.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 8 at 15:39









          José Carlos SantosJosé Carlos Santos

          157k22126227




          157k22126227








          • 2




            $begingroup$
            Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
            $endgroup$
            – Jonathan Baram
            Jan 8 at 15:43














          • 2




            $begingroup$
            Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
            $endgroup$
            – Jonathan Baram
            Jan 8 at 15:43








          2




          2




          $begingroup$
          Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
          $endgroup$
          – Jonathan Baram
          Jan 8 at 15:43




          $begingroup$
          Thank you, I also found that the sum of the x-axis and the y-axis is equal to the whole plane for a more simple example
          $endgroup$
          – Jonathan Baram
          Jan 8 at 15:43


















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