On the integration of vector-valued functions
泛函分析
2016-09-06 v1
摘要
We discuss relationships between the McShane, Pettis, Talagrand and Bochner integrals. A large number of different methods of integration of Banach-space-valued functions have been introduced, based on the various possible constructions of the Lebesgue integral. They commonly run fairly closely together when the range space is separable (or has w^*-separable dual) and diverge more or less sharply for general range spaces. The McShane integral as described by [Go] is derived from the `gauge-limit' integral of [McS]. Here we give both positive and negative results concerning it and the other three integrals listed above.
引用
@article{arxiv.math/9202202,
title = {On the integration of vector-valued functions},
author = {D. H. Fremlin and Jose Mendoza},
journal= {arXiv preprint arXiv:math/9202202},
year = {2016}
}