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Jun
29 |
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Naive definition of surface area doesn't work?
Perhaps one needs to add that the vertical and the horizontal legs tend to zero "uniformly" in some sense... Where is this written? |
Jun
29 |
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Naive definition of surface area doesn't work?
@BenoîtKloeckner, as far as I understand it is sufficient to claim that the corresponding triangles in the set of parameters are right (i.e. one of their angles is right) and their legs are parallel to the coordinate lines. Is it true? |
Jun
20 |
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Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Federico, as far as I understand, the problem with the equivalence of these two axioms arises when we define polytopes as compact sets (spanned by... etc), then $P\setminus Q$ needs not to be a polytope, and the functional $V_n$ is not defined on $P\setminus Q$. |
Jun
20 |
revised |
Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
added 62 characters in body |
Jun
20 |
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Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Even for the dimension $n=3$ this trick becomes bulky. To say nothing about $n>3$. Or I don't know something? Anyway this looks like a new invention of bicycle. It's difficult to believe that nobody did this before. |
Jun
20 |
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Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Thank you, Liviu. I am reading this. |
Jun
20 |
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Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Is it possible that this wasn't proved in textbooks? |
Jun
20 |
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Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Eric, I don't understand. Do you mean that for proving this it is nesessary to extend $V_n$ to the Jordan (or Lebesgue) measure (and only after that this becomes evident)? I believe there is a simple trick that allows to prove this without going to Jordan. |
Jun
20 |
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Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
I meant, disappeared from the list of the questions on the main page. I thought, this means that nobody is interested. |
Jun
20 |
comment |
Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Perhaps, this is my bad English. What is it called when something appears and disappears immediately? |
Jun
20 |
asked | Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height |
Jun
5 |
awarded | Inquisitive |
Jun
4 |
revised |
Analogs of the paralleloram identity in higher degrees
added 2 characters in body |
Jun
4 |
asked | Analogs of the paralleloram identity in higher degrees |
May
23 |
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Correspondence between real forms and real structures on complex Lie groups
@MikhailBorovoi, excuse me, I did not understand, for which class of groups this is a one-to-one correspondence? And is this a folklore, or there exist references? |
May
22 |
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Correspondence between real forms and real structures on complex Lie groups
@YCor: Yes, I thought the same, an involutive anti-linear Lie algebra automorphism. So this is not a one-to-one correspondence?... I think, at least for reductive groups (i.e. for complexifications of compact real Lie groups) this must be so... That's true? |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
added 57 characters in body |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
added 3 characters in body |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
added 114 characters in body |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
edited body |