数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2004年
3期
250-258
,共9页
强Mcshane积分%Mcshane积分%Bochner积分
彊Mcshane積分%Mcshane積分%Bochner積分
강Mcshane적분%Mcshane적분%Bochner적분
strong McShane integral%McShane integral%Bochner integral
在本文中,我们定义和研究了I0Rm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.
在本文中,我們定義和研究瞭I0Rm到Banach空間X中函數的彊McShane積分,直接證明瞭彊Mcshane積分與Bochner積分是等價的,McShane積分與彊Mcshane積分等價噹且僅噹Banach空間X有限維. 從而部分地迴答瞭R.A.Gordon的一箇公開問題.
재본문중,아문정의화연구료I0Rm도Banach공간X중함수적강McShane적분,직접증명료강Mcshane적분여Bochner적분시등개적,McShane적분여강Mcshane적분등개당차부당Banach공간X유한유. 종이부분지회답료R.A.Gordon적일개공개문제.
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.
