共查询到20条相似文献,搜索用时 62 毫秒
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模糊Choquet-可积函数空间的凸锥结构 总被引:1,自引:0,他引:1
在一般有限模糊测度空间上研究了非负模糊Choquet-可积函数的模糊测度表示, 进而获得了非负模糊Choquet-可积函数空间和一般模糊Choquet-可积函数空间构成凸锥的充要条件. 相似文献
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讨论闭区间上有无穷多个不连续点的有界函数的可积问题,所得结果是"闭区间上不连续的点仅有有限个的函数可积"的推广. 相似文献
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一致可积函数的非标准刻画 总被引:2,自引:1,他引:1
设(X,A,μ)是内有限可加测度空间.首先给出了S-可积的等价条件,进而给出了一致可积函数的非标准刻画,即可测函数集{fi)i∈I是一致可积的当且仅当对于任意的i∈*I,fi都是S-可积的. 相似文献
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对(1+1)维可积系统,本文在零曲率方程表示理论框架内,给出统一的方法去构造和高阶约束相联系的有限维可积系统,导出这些系统的守恒积分的生成函数,证明它们的可积性,并进而把一族(1+1)维可积系统中的每一个方程分解为两个可交换的有限维可积的Hamilton系统。 相似文献
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本文利用有界函数黎曼可积的充要条件讨论了某些复合函数的黎曼可积性,给出了外函数黎曼可积,内函数连续,复合函数不一定黎曼可积的例子. 相似文献
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从一个特征值问题出发,首先推导一族非线性发展方程,其中包括著名MKdV方程做为特殊约化,进一步证明这族方程在Liounille意义下可积并具有Bi-Hamilton结构,而在位执函数和特征函数之间的一定约束下,特征值问题被非线性化为一完全可积的有限维Hamilton系统。 相似文献
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Properties of Lebesgue function for Lagrange interpolation on equidistant nodes are investigated. It is proved that Lebesgue function can be formulated both in terms of a hypergeometric function 2F1 and Jacobt polynomials. Moreover, an integral expression of Lebesgue function is also obtained and the asymptotic behavior of Lebesgue constant is studied. 相似文献
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证明了非负有界函数的Lebesgue上积分等于函数下方图形的Lebesgue外测度,其Lebesgue下积分等于函数下方图形的Lebesgue内测度,从而将积分的几何意义从可测情形推广到一般情形. 相似文献
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Selma Özça? 《Topology and its Applications》2009,156(18):3021-3028
The author introduces the notions of Lebesgue di-uniformity and co Lebesgue di-uniformity and investigates the relationship between a Lebesgue quasi uniformity on X and the corresponding Lebesgue di-uniformity on the discrete texture (X,P(X)). Finally a notion of a dual dicovering Lebesgue quasi di-uniform texture space is introduced and several properties are discussed. 相似文献
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Long Huang & Dachun Yang 《数学研究》2021,54(3):262-336
The targets of this article are threefold. The first one is to give a survey on the
recent developments of function spaces with mixed norms, including mixed Lebesgue
spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and mixed
Morrey spaces as well as anisotropic mixed-norm Hardy spaces. The second one is
to provide a detailed proof for a useful inequality about mixed Lebesgue norms and
the Hardy–Littlewood maximal operator and also to improve some known results on
the maximal function characterizations of anisotropic mixed-norm Hardy spaces and
the boundedness of Calderón–Zygmund operators from these anisotropic mixed-norm Hardy spaces to themselves or to mixed Lebesgue spaces. The last one is to correct
some errors and seal some gaps existing in the known articles. 相似文献
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Our aim is to introduce the grand Bochner–Lebesgue space in the spirit of Iwaniec–Sbordone spaces, also known as grand Lebesgue spaces, and prove some of its properties. We will also deal with the associate space for grand Bochner–Lebesgue spaces. 相似文献
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Pankaj Jain Arun Pal Singh Monika Singh Vladimir D. Stepanov 《Mathematische Nachrichten》2019,292(4):841-849
The aim of this paper is to extend Sawyer's duality principle from the cone of decreasing functions of the Lebesgue space to the cone of decreasing functions of the grand Lebesgue space and to prove the boundedness of classical Hardy operators in the grand Lebesgue spaces. 相似文献
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F. Chorlton 《International Journal of Mathematical Education in Science & Technology》2013,44(2):315-323
In this note the measure problem for the Lebesgue measure is discussed in terms of metric space theory. It is illuminated that under the axiom of choice most of the subsets of [0, 1) with positive outer measure are non‐Lebesgue measurable. This fact is adequate to emphasize the significance of Lebesgue measurability as well as the essentiality of the axiom of choice. 相似文献
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A new definition of integral-like functionals exploiting the ideas of the Lebesgue integral construction and extending the idea of pan-integrals is given. Some convergence theorems for sequence of measurable functions are discussed. As a result, a theoretical basis for applications of the generalized Lebesgue integral is provided. Several types of integrals known from the literature are shown to be special cases of generalized Lebesgue integral. 相似文献