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2d

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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? 
2d

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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
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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 
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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
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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 onetoone 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 antilinear Lie algebra automorphism. So this is not a onetoone 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
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May 22 
revised 
Correspondence between real forms and real structures on complex Lie groups
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May 22 
revised 
Correspondence between real forms and real structures on complex Lie groups
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May 22 
revised 
Correspondence between real forms and real structures on complex Lie groups
edited body 