On The Integration Of Vector-Valued Functions
ILLINOIS JOURNAL OF MATHEMATICS(1994)
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.
更多查看译文
关键词
bochner integral,value function,banach space,functional analysis
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络