Ball volume - Axioms of Choice

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Ball volume

Set

context

$p\in \mathbb N$

definiendum	$V_p:\mathbb R_+\to \mathbb R_+$
definiendum	$V_p(r):=\beta^p(B_0(r))$

Discussion

Theorems

For all $a\in \mathbb R^p$ , the volume of the ball $B_a(r)$ is the same and given by

$V_p(r)= \pi^{p/2}\ \Gamma(p/2+1)^{-1}\ r^p$

Reference

Wikipedia: Volume of an n-ball

Parents

Context

Lebesgue-Borel measure, Open ball

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