Volumes of Generalized Balls. Gao, F. American Mathematical Monthly, 120(2):130-130, 2013-02-01T00:00:00.
abstract   bibtex   
A concise proof is presented for the known formula (see [1], [2], [3]) of the volume of

B(t) = (x 1, x 2,…, x n ) ∈ R n : |x 1| p1 + |x 2| p2 + · · · + |x n | pn t.

The derivation assumes a familiarity with the properties of both the gamma function and the exponential distribution.
@article{Gao:2013-02-01T00:00:00:0002-9890:130,
	Abstract = {A concise proof is presented for the known formula (see [<b>1</b>], [<b>2</b>], [<b>3</b>]) of the volume of<br></br>
<i>B</i>(<i>t</i>) = {(<i>x</i>
<sub>1</sub>, <i>x</i>
<sub>2</sub>,&#8230;, <i>x</i>
<sub>
<i>n</i>
</sub>) &#8712; R<sup>
<i>n</i>
</sup> : |<i>x</i>
<sub>1</sub>|<sup>
<i>p</i>1</sup>
+ |<i>x</i>
<sub>2</sub>|<sup>
<i>p</i>2</sup> + · · · + |<i>x</i>
<sub>
<i>n</i>
</sub>|<sup>
<i>pn</i>
</sup> &#8804; <i>t</i>}.<br></br>The derivation assumes a familiarity with the properties of both the gamma function and the exponential distribution.},
	Author = {Gao, Fuchang},
	Date-Added = {2015-04-30 13:52:47 +0000},
	Date-Modified = {2015-04-30 13:52:54 +0000},
	Journal = {American Mathematical Monthly},
	Number = {2},
	Pages = {130-130},
	Title = {Volumes of Generalized Balls},
	Volume = {120},
	Year = {2013-02-01T00:00:00},
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