Calculate Lebesgue and Hausdorf measure of a hexagon
Given this hexagon $P$, I've got to calculate the Lebesgue measure $lambda_{2}(P)$ and the Hausdorff measure $mathscr{H}^1(partial P)$. My thoughts are:
You can leave out the 6 line segments of length 1 that makes the boundary, as they are presentable as graph of a steady function (so their lebesgue measure is zero).My intuition tells me that $lambda_{2}(P)=6*frac{sqrt{3}}{4}= frac{3sqrt{3}}{2}$ ( as one triangle has one triangle has the area:$frac{sqrt{3}}{4}$) and $mathscr{H}^1(partial P)=6$(the lenght of the boundary). I'm not sure if it's right and how to argue the right results. Any help would be greatly aprpreciated.
measure-theory lebesgue-measure hausdorff-measure
asked Nov 28 '18 at 16:14
Thesinus
245210
add a comment |
Given this hexagon $P$, I've got to calculate the Lebesgue measure $lambda_{2}(P)$ and the Hausdorff measure $mathscr{H}^1(partial P)$. My thoughts are:
You can leave out the 6 line segments of length 1 that makes the boundary, as they are presentable as graph of a steady function (so their lebesgue measure is zero).My intuition tells me that $lambda_{2}(P)=6*frac{sqrt{3}}{4}= frac{3sqrt{3}}{2}$ ( as one triangle has one triangle has the area:$frac{sqrt{3}}{4}$) and $mathscr{H}^1(partial P)=6$(the lenght of the boundary). I'm not sure if it's right and how to argue the right results. Any help would be greatly aprpreciated.
measure-theory lebesgue-measure hausdorff-measure
asked Nov 28 '18 at 16:14
Thesinus
245210
add a comment |
Given this hexagon $P$, I've got to calculate the Lebesgue measure $lambda_{2}(P)$ and the Hausdorff measure $mathscr{H}^1(partial P)$. My thoughts are:
You can leave out the 6 line segments of length 1 that makes the boundary, as they are presentable as graph of a steady function (so their lebesgue measure is zero).My intuition tells me that $lambda_{2}(P)=6*frac{sqrt{3}}{4}= frac{3sqrt{3}}{2}$ ( as one triangle has one triangle has the area:$frac{sqrt{3}}{4}$) and $mathscr{H}^1(partial P)=6$(the lenght of the boundary). I'm not sure if it's right and how to argue the right results. Any help would be greatly aprpreciated.
measure-theory lebesgue-measure hausdorff-measure
asked Nov 28 '18 at 16:14
Thesinus
245210
Given this hexagon $P$, I've got to calculate the Lebesgue measure $lambda_{2}(P)$ and the Hausdorff measure $mathscr{H}^1(partial P)$. My thoughts are:
You can leave out the 6 line segments of length 1 that makes the boundary, as they are presentable as graph of a steady function (so their lebesgue measure is zero).My intuition tells me that $lambda_{2}(P)=6*frac{sqrt{3}}{4}= frac{3sqrt{3}}{2}$ ( as one triangle has one triangle has the area:$frac{sqrt{3}}{4}$) and $mathscr{H}^1(partial P)=6$(the lenght of the boundary). I'm not sure if it's right and how to argue the right results. Any help would be greatly aprpreciated.
measure-theory lebesgue-measure hausdorff-measure
measure-theory lebesgue-measure hausdorff-measure
asked Nov 28 '18 at 16:14
Thesinus
245210
asked Nov 28 '18 at 16:14
Thesinus
245210
asked Nov 28 '18 at 16:14
Thesinus
245210
asked Nov 28 '18 at 16:14
Thesinus
245210
asked Nov 28 '18 at 16:14
Thesinus
245210
245210
add a comment |
add a comment |
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