Title

On the degree of weak convergence of a sequence of finite measures to the unit measure under convexity

Abstract

This is a study of the degree of weak convergence under convexity of a sequence of finite measures μj on Rk, k ≥ 1, to the unit measure δx0. LetQ denote a convex and compact subset of Rk, let f{hook} ε{lunate} Cm(Q), m ≥ 0, satisfy a convexity condition and let μ be a finite measure on Q. Using standard moment methods, upper bounds and best upper bounds are obtained for |∝Qf{hook}dμ - f{hook}(x0)|. They sometimes lead to sharp inequalities which are attained for particular μ and f{hook}. These estimates are better than the corresponding ones found in the literature. © 1987.

Publication Title

Journal of Approximation Theory

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