On Abstract Numerical Integrations

Abstract

Let X be a s pace of func tions, say X c C(K), K locally co mpact Hausdorff, le t IEX* be an int~gral on X and le t M* C X* be a given subspace of "simple" functiona ls, then it is des ired to obta in!!n leM~ for given n, leM";, C M*; M";, bein g a su itable" dim ens ion a l s llb s pace d e t e rmin ed so th a t: I I annihi lates a given finit e dim ensiona l subs pace X, C X. In thi s ge neral context , the abst ract ana lysis of nllm e ri ca l integration is de ve loped and ce rtain speci fi c app licatio ns are made.