共查询到18条相似文献,搜索用时 78 毫秒
1.
R.AGordon在[1]中定义了从R1到Banach空间抽象函数的McShane积分,证明了当X不含C0时,如果f在[a,b]上McShanef可积,则在[a,b]上Petits 可积.在这篇文章中,我们定义了从Rn到Banaach空间抽象函数的Mcshane积分,证明了fMcShane可积,则f是Pattis可积.于是我们推广了[1]的结果. 相似文献
2.
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. 相似文献
3.
4.
引入向量值函数关于实值函数的Riemann-Stieltjes积分,给出了向量值Riemann-Stieltjes可积的充要条件,并讨论了积分的收敛定理. 相似文献
5.
一维空间R中的Jensen不等式在概率论与鞅论等学科中都有着广泛的应用.本文以锥为工具,将这个著名的不等式推广到序Banach空间,得出向量值的Bochner积分型的广义Jensen不等式. 相似文献
6.
本文证明了如果X是不含c0的Banach空间,f是定义在区间I0包含R^m上取值于Panach空间X的函数,并且,在I0上Henstock可积,则总存在I0的一个非退化子区间J,使得f在J上McShane可积,从而对Kartak的一个问题作出了肯定的回答. 相似文献
7.
引进偏Bochner积分的概念.证明了在不可分清形下,偏Bochner积分与Bochner积分有本质的差异.作为应用,通过向量测度空间用价Bochner积分给出了Radon-Nikodym性质的一个刻划. 相似文献
8.
在研究Bochner可积函数空间上线性算子的积分表示时,一般总要求函数值域空间X具有Radon-Nikodym性质.本文从线性算子本身出发,在不要求X具有Radon-Nikodym性质的条件下研究线性算子的积分表示,给出一个充要条件. 相似文献
9.
Mcshane积分与可测函数许东福(集美师范专科学校)1958/57年,R·Henstock与J.Kurzweil分别给出一种Riemann完全型的积分[4],人们称为Henstock-Kurzweil积分(简记为H-积分)。它推广了Lebesgue... 相似文献
10.
我们给出每个绝对Henstock可积函数都是Mcshane可积的一个新的证明。 相似文献
11.
José Rodríguez 《Journal of Mathematical Analysis and Applications》2006,316(2):579-600
Let (Ω,Σ,μ) be a complete probability space and an absolutely summing operator between Banach spaces. We prove that for each Dunford integrable (i.e., scalarly integrable) function the composition u○f is scalarly equivalent to a Bochner integrable function. Such a composition is shown to be Bochner integrable in several cases, for instance, when f is properly measurable, Birkhoff integrable or McShane integrable, as well as when X is a subspace of an Asplund generated space or a subspace of a weakly Lindelöf space of the form C(K). We also study the continuity of the composition operator f?u○f. Some other applications are given. 相似文献
12.
The Mcshane Integral of Fuzzy-Valued Functions 总被引:3,自引:0,他引:3
In this paper, the Mcshane integrals of fuzzy-valued functions are defined, discussed, and characterized. It shows that, in a sense, the Mcshane integrals of interval-valued functions and fuzzy-valued functions are the Riemann-type definitions of the Aumann integral and (K) integral respectively.AMS Subject Classification (2000) 28EI0 (04A72)The authors are supported by the Special Fund of China for Ph.D. Instructors in Universities 相似文献
13.
The aim of this paper is to study Birkhoff integrability for multi-valued maps , where (Ω,Σ,μ) is a complete finite measure space, X is a Banach space and cwk(X) is the family of all non-empty convex weakly compact subsets of X. It is shown that the Birkhoff integral of F can be computed as the limit for the Hausdorff distance in cwk(X) of a net of Riemann sums ∑nμ(An)F(tn). We link Birkhoff integrability with Debreu integrability, a notion introduced to replace sums associated to correspondences when studying certain models in Mathematical Economics. We show that each Debreu integrable multi-valued function is Birkhoff integrable and that each Birkhoff integrable multi-valued function is Pettis integrable. The three previous notions coincide for finite dimensional Banach spaces and they are different even for bounded multi-valued functions when X is infinite dimensional and X∗ is assumed to be separable. We show that when F takes values in the family of all non-empty convex norm compact sets of a separable Banach space X, then F is Pettis integrable if, and only if, F is Birkhoff integrable; in particular, these Pettis integrable F's can be seen as single-valued Pettis integrable functions with values in some other adequate Banach space. Incidentally, to handle some of the constructions needed we prove that if X is an Asplund Banach space, then cwk(X) is separable for the Hausdorff distance if, and only if, X is finite dimensional. 相似文献
14.
We study the Pettis integral for multi-functions defined on a complete probability space (Ω,Σ,μ) with values into the family cwk(X) of all convex weakly compact non-empty subsets of a separable Banach space X. From the notion of Pettis integrability for such an F studied in the literature one readily infers that if we embed cwk(X) into ?∞(BX∗) by means of the mapping defined by j(C)(x∗)=sup(x∗(C)), then j○F is integrable with respect to a norming subset of B?∞∗(BX∗). A natural question arises: When is j○F Pettis integrable? In this paper we answer this question by proving that the Pettis integrability of any cwk(X)-valued function F is equivalent to the Pettis integrability of j○F if and only if X has the Schur property that is shown to be equivalent to the fact that cwk(X) is separable when endowed with the Hausdorff distance. We complete the paper with some sufficient conditions (involving stability in Talagrand's sense) that ensure the Pettis integrability of j○F for a given Pettis integrable cwk(X)-valued function F. 相似文献
15.
A. Avilés 《Journal of Functional Analysis》2010,259(11):2776-2792
Di Piazza and Preiss asked whether every Pettis integrable function defined on [0,1] and taking values in a weakly compactly generated Banach space is McShane integrable. In this paper we answer this question in the negative. Moreover, we give a counterexample where the target Banach space is reflexive. 相似文献
16.
Several results about convolution and about Fourier coefficients for X-valued functions defined on t he torus satisfying the condition sup ||y||=1∫-π^π|| B (f (e^iθ), y)||dθ/2π〈 ∞ for a bounded bilinear map B : X × Y → Z are presented and some applications are given. 相似文献
17.
V. Marraffa 《Journal of Mathematical Analysis and Applications》2004,293(1):71-78
Absolutely summing operators between Banach spaces are characterized by means of McShane integrable functions. 相似文献
18.
Afif Ben Amar 《Numerical Functional Analysis & Optimization》2013,34(11):1213-1220
We present some new variants of Leray–Schauder type fixed point theorems and eigenvalue results for decomposable single-valued nonlinear weakly compact operators in Dunford-Pettis spaces. 相似文献