Averaging sets: A generalization of mean values and spherical designs

Abstract

: [0, 1 ] + R, one cannot of course expect there to be a single point x at which every one assumes its mean value, but there is an easy generalization in terms of weighted averages: there exist at most m points xi and positive weights oi summing to 1 so that \’ aifj(Xi) = I”fi dt for j = 1, 2 ,..., m.