McShane equi-integrability and Vitali’s convergence theorem
نویسندگان
چکیده
منابع مشابه
On the Notion of Uniform Integrability and Mean Convergence Theorem for Fuzzy Random Variables
In this paper the convergence criterion of fuzzy random variable is investigated. An attempt is made to study the equivalence relation of uniform integrability of fuzzy random variables. Mean convergence theorem, Lebesgue dominated convergence theorem and Mean Ergodic theorem for the case of fuzzy random variable are introduced.
متن کاملUniform Integrability and the Pointwtse Ergodic Theorem
Let iX, 03, m) be a finite measure space. We shall denote by L*im) (1 èp< °°) the Banach space of all real-valued (B-measurable functions/ defined on X such that |/[ p is m-integrable, and by L°°(w) the Banach space of all real-valued, (B-measurable, w-essentially bounded functions defined on X; as usual, the norm in Lpim) is given by 11/11,.= {fx\fix)\pdm}1'*, and the norm in Lxim) by \\g\\x =...
متن کاملEqui-integrability results for 3D-2D dimension reduction problems
3D-2D asymptotic analysis for thin structures rests on the mastery of scaled gradients ( ∇αuε ∣∣ 1 ε ∇3uε ) bounded in L(Ω;R), 1 < p < +∞. Here it is shown that, up to a subsequence, uε may be decomposed as wε+zε, where zε carries all the concentration effects, i.e. ∣∇αwε| 1ε∇3wε )∣∣p} is equi-integrable, and wε captures the oscillatory behavior, i.e. zε → 0 in measure. In addition, if {uε} is ...
متن کاملA Note on Equi-integrability in Dimension Reduction Problems
A very handy tool in the study of the asymptotic behavior of variational problems defined on Sobolev spaces is Fonseca, Müller and Pedregal’s equi-integrability Lemma [8] (see Theorem 2.1 below; see also earlier work by Acerbi and Fusco [2] and by Kristensen [11]), which allows to substitute a sequence (wj) with (∇wj) bounded in L by a sequence (zj) with (|∇zj | ) equi-integrable, such that the...
متن کاملA new proof for the Banach-Zarecki theorem: A light on integrability and continuity
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2004
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2004.133903