Rm上Banach-值函数的强McShane积分

摘要

在本文中,我们定义和研究了I0Rm到Banach空间X中函数的强McShane积分,直接证明了强Mcshane积分与Bochner积分是等价的,McShane积分与强Mcshane积分等价当且仅当Banach空间X有限维. 从而部分地回答了R.A.Gordon的一个公开问题.%In this paper we define and study the strong McShane integral of functions mapping a compact interval I0 in Rm into Banach spaces X. We directly prove that the strong McShane integral and the Bochner integral are equivalent, and the McShane integral and the strong McShane integral are equivalent if and only if the Banach spaces are finite dimensional. This partially gives a positive answer to an open problem of R.A.Gordon.