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Jun
20 |
comment |
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
added 2 characters in body |
Jun
4 |
asked | Analogs of the paralleloram identity in higher degrees |
May
23 |
comment |
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 |
May
22 |
comment |
Correspondence between real forms and real structures on complex Lie groups
@YCor: Pardon, I corrected the text in MSE (and here also). |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
added 538 characters in body |
May
22 |
comment |
Correspondence between real forms and real structures on complex Lie groups
Does this give an answer in the case, when $K$ is a compact real Lie group and $G$ is its complexification? |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
edited title |