Compute Measures (Length, Area, Volume, etc.) 

The measure of a region corresponds to length of a curve, area of a surface, and volume of a solid. But it also generalizes to zero-dimensional objects where the measure is counted, as well as -dimensional objects where the measure is a generalized volume. For a region containing parts with different dimensions, the measure is taken to be the one that corresponds to the maximal dimension, and the measure is given by the integral , where is the region.

Curve lengths.

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Surface areas.

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Solid volumes.

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General -dimensional measures for unit spheres, balls, and simplices.

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