What is the maximum volume of lebesgue measurable set $Asubseteq [0,6]$ such that…

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$textI came accross an interesting question:$



$ $



$textWhat is the maximum volume of a lebesgue measurable set Asubseteq[0,6]^2 text such that: $



$A cap bigl(A+binom 12bigl)=emptyset $



$textI got only to 5pi text but the answer is 24. What am I missing?$




real-analysis lebesgue-measure volume




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  • 1




    Could you say a rough word on how you got $5pi$?
    – Arnaud Mortier
    7 hours ago










  • What if $A=[0,6]^2setminus (1,2)$? Maybe you mean $cup$ instead of $cap$?
    – Arnaud Mortier
    6 hours ago











  • @ArnaudMortier Sorry I mistranslated the question, see edit :)
    – Gil Or
    6 hours ago











  • It makes more sense now, but still... $5pi$?
    – Arnaud Mortier
    6 hours ago










  • @ArnaudMortier I just thought about the open circle: $(x-a)^2+(x-b)^2 < 5$ that is inside $[0,6]^2$. I mean, if (a+1, b+2) > (x,y) for (x,y) $in$ A
    – Gil Or
    6 hours ago














up vote
1
down vote

favorite












$textI came accross an interesting question:$



$ $



$textWhat is the maximum volume of a lebesgue measurable set Asubseteq[0,6]^2 text such that: $



$A cap bigl(A+binom 12bigl)=emptyset $



$textI got only to 5pi text but the answer is 24. What am I missing?$




real-analysis lebesgue-measure volume




share|cite|improve this question

















  • 1




    Could you say a rough word on how you got $5pi$?
    – Arnaud Mortier
    7 hours ago










  • What if $A=[0,6]^2setminus (1,2)$? Maybe you mean $cup$ instead of $cap$?
    – Arnaud Mortier
    6 hours ago











  • @ArnaudMortier Sorry I mistranslated the question, see edit :)
    – Gil Or
    6 hours ago











  • It makes more sense now, but still... $5pi$?
    – Arnaud Mortier
    6 hours ago










  • @ArnaudMortier I just thought about the open circle: $(x-a)^2+(x-b)^2 < 5$ that is inside $[0,6]^2$. I mean, if (a+1, b+2) > (x,y) for (x,y) $in$ A
    – Gil Or
    6 hours ago












up vote
1
down vote

favorite









up vote
1
down vote

favorite











$textI came accross an interesting question:$



$ $



$textWhat is the maximum volume of a lebesgue measurable set Asubseteq[0,6]^2 text such that: $



$A cap bigl(A+binom 12bigl)=emptyset $



$textI got only to 5pi text but the answer is 24. What am I missing?$




real-analysis lebesgue-measure volume




share|cite|improve this question













$textI came accross an interesting question:$



$ $



$textWhat is the maximum volume of a lebesgue measurable set Asubseteq[0,6]^2 text such that: $



$A cap bigl(A+binom 12bigl)=emptyset $



$textI got only to 5pi text but the answer is 24. What am I missing?$





real-analysis lebesgue-measure volume





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 6 hours ago
























asked 7 hours ago









Gil Or

623




623







  • 1




    Could you say a rough word on how you got $5pi$?
    – Arnaud Mortier
    7 hours ago










  • What if $A=[0,6]^2setminus (1,2)$? Maybe you mean $cup$ instead of $cap$?
    – Arnaud Mortier
    6 hours ago











  • @ArnaudMortier Sorry I mistranslated the question, see edit :)
    – Gil Or
    6 hours ago











  • It makes more sense now, but still... $5pi$?
    – Arnaud Mortier
    6 hours ago










  • @ArnaudMortier I just thought about the open circle: $(x-a)^2+(x-b)^2 < 5$ that is inside $[0,6]^2$. I mean, if (a+1, b+2) > (x,y) for (x,y) $in$ A
    – Gil Or
    6 hours ago












  • 1




    Could you say a rough word on how you got $5pi$?
    – Arnaud Mortier
    7 hours ago










  • What if $A=[0,6]^2setminus (1,2)$? Maybe you mean $cup$ instead of $cap$?
    – Arnaud Mortier
    6 hours ago











  • @ArnaudMortier Sorry I mistranslated the question, see edit :)
    – Gil Or
    6 hours ago











  • It makes more sense now, but still... $5pi$?
    – Arnaud Mortier
    6 hours ago










  • @ArnaudMortier I just thought about the open circle: $(x-a)^2+(x-b)^2 < 5$ that is inside $[0,6]^2$. I mean, if (a+1, b+2) > (x,y) for (x,y) $in$ A
    – Gil Or
    6 hours ago







1




1




Could you say a rough word on how you got $5pi$?
– Arnaud Mortier
7 hours ago




Could you say a rough word on how you got $5pi$?
– Arnaud Mortier
7 hours ago












What if $A=[0,6]^2setminus (1,2)$? Maybe you mean $cup$ instead of $cap$?
– Arnaud Mortier
6 hours ago





What if $A=[0,6]^2setminus (1,2)$? Maybe you mean $cup$ instead of $cap$?
– Arnaud Mortier
6 hours ago













@ArnaudMortier Sorry I mistranslated the question, see edit :)
– Gil Or
6 hours ago





@ArnaudMortier Sorry I mistranslated the question, see edit :)
– Gil Or
6 hours ago













It makes more sense now, but still... $5pi$?
– Arnaud Mortier
6 hours ago




It makes more sense now, but still... $5pi$?
– Arnaud Mortier
6 hours ago












@ArnaudMortier I just thought about the open circle: $(x-a)^2+(x-b)^2 < 5$ that is inside $[0,6]^2$. I mean, if (a+1, b+2) > (x,y) for (x,y) $in$ A
– Gil Or
6 hours ago




@ArnaudMortier I just thought about the open circle: $(x-a)^2+(x-b)^2 < 5$ that is inside $[0,6]^2$. I mean, if (a+1, b+2) > (x,y) for (x,y) $in$ A
– Gil Or
6 hours ago















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