Abstract and Applied Analysis
Volume 5 (2000), Issue 4, Pages 207-226
Integration with respect to a vector measure and function
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, C amino de Vera, Valencia 14 46022, Spain
Received 13 May 2000
Copyright © 2000 L. M. García-Raffi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The integration with respect to a vector measure may be applied in order to approximate a function in a Hilbert space by means of a finite orthogonal sequence attending to two different error criterions. In particular, if is a Lebesgue measurable set, , and is a finite family of disjoint subsets of , we can obtain a measure and an approximation satisfying the following conditions: (1) is the projection of the function in the subspace generated by in the Hilbert space . (2) The integral distance between and on the sets is small.