Fun fact from @eigenstate : high dimensional bread volume is mostly concentrated to the crusts,
Well, strictly speaking, it depends on what sort of volume you mean; if you're sufficiently open-minded about the use of the word, it can even all be concentrated right at the center. But yes, @eigenstate is right, in a general moral sense. As usual.
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I refuse to call the Euler characteristic a volume, even I am not categorical enough for that
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Frankly, I was thinking of those measures whose support consists of a single point; I too would regard it as a barbarous liberty to call the Euler characteristic a volume.
End of conversation
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