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An asymptotic formula is proved for the expected $T$-functional of the convexhull of independent and identically distributed random points sampled from theEuclidean unit sphere in $\mathbb{R}^n$ according to an arbitrary positivecontinuous density. As an application, the approximation of the sphere byrandom polytopes in terms of $L_p$ surface area differences is discussed.

Asymptotic expected $T$-functionals of random polytopes with applications to $L_p$ surface areas