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Mathematics-Online lexicon:

Approximation of Volume

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For a regular region $ V$ the volume can be defined by approximation using a sequence of polygonal regions $ V_n$ with $ \operatorname{dist}_H (V_n,V)\to 0$:

$\displaystyle \operatorname{vol} V =
\lim_{n\to\infty} \operatorname{vol} V_n

The limit exists because of the piecewise continuity of the boundary curves of $ V$ and it is independent from the chosen sequence $ (V_n)$.

(Authors: Höllig/Streit/Höfert)

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  automatically generated 8/ 4/2008