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
Recommended Citation
Anastassiou, G. (1987). On the degree of weak convergence of a sequence of finite measures to the unit measure under convexity. Journal of Approximation Theory, 51 (4), 333-349. https://doi.org/10.1016/0021-9045(87)90042-6
