Spherical Measure
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High Quality Content by WIKIPEDIA articles! In mathematics specifically, in geometric measure theory spherical measure n is the natural Borel measure on the n-sphere Sn. Spherical measure is often normalized so that it is a probability measure on the sphere, i.e. so that n(Sn) = 1. There are several ways to define spherical measure. One way is to use the usual round or arclength metric n on Sn; that is, for points x and y in Sn, n(x, y) is defined to be the (Euclidean) angle that they subtend at the centre of the sphere (the origin of Rn+1). Now construct n-dimensional Hausdorff measure Hn on ...
High Quality Content by WIKIPEDIA articles! In mathematics specifically, in geometric measure theory spherical measure n is the natural Borel measure on the n-sphere Sn. Spherical measure is often normalized so that it is a probability measure on the sphere, i.e. so that n(Sn) = 1. There are several ways to define spherical measure. One way is to use the usual round or arclength metric n on Sn; that is, for points x and y in Sn, n(x, y) is defined to be the (Euclidean) angle that they subtend at the centre of the sphere (the origin of Rn+1). Now construct n-dimensional Hausdorff measure Hn on the metric space (Sn, n) and define sigma^{n} = frac{1}{H^{n}(mathbf{S}^{n})} H^{n}.
