Some topics concerning integrals of derivatives and difference quotients on metric spaces
نویسنده
چکیده
where σn−1 denotes the surface measure of the unit sphere S n−1 = {z ∈ R : |z| = 1}, and |z| denotes the standard Euclidean norm of z ∈ R. This formula is given in equation (18) on p125 of [Ste1], and it is proved by using the Fundamental Theorem of Calculus to first write f(x) as the integral along any ray emanating from x of the directional derivative of f in the direction of the ray, and then averaging over all such rays. In particular,
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