测度

We study also the corresponding Cauchy problems with a given generalized Borel measure as initial data.

情形，证明了以外正则Borel测度作为初始值的Cauchy问题解的存在性。

We prove that on the localgauge group C∞(M a compact manifold,G a matrix Lie group)there does not exist afinite translationally invariant Borel measure.

我们证明了在局域规范群C∽(M为一紧致流形，G为一矩阵李群)上不存在有限的平移不变的Borel测度。

Finally,we discuss the existence of symmetric positive solutions for p-Laplacian two point boundary value problem on time scales.

最后，讨论了测度链上p-拉普拉斯动力方程两点边值问题的正对称解的存在性。

This paper gives a concept of Lebesgue-Stieltjes measure in monotone increasing left continuous bounded function and discuss some properties.

以单调递增左连续有界函数 f 给出了 Lebesgue-Stieltjes测度的概念，进一步讨论了由它产生的若干相应的性

In this paper,a proof is made of the equivalence in three definitions of the integral of bounded function in finite set measure.

关于Lebesgue积分，文献有不同的定义，本文给出了测度有限集上有界函数 Lebesgue积分三种不同定义的等价性的一种证明。

It also gets a unified condition which has a wider range than regulated function and comes to the conclusion that the function of bounded variation is the integrable function of Riemann.

通过定义多维零测度集将可积函数的特征扩展到多维情形，同样统一了多维情形的充分条件，建立了多维情形的可积性理论。

We first show some properties of such operators and give an explit description about the image of a linear bounded operator on a linear normed space. Then based on these results, we show the mean ergordic theorem on a C*-bial-gebra and get a sufficient and necessary condition for a linear functional to be Haar measure. Finally we discuss the sufficent conditions for the existence of Haar measure on C*-bialgebras.

本文首先通过考察这样算子的性质和刻画赋范线性空间中连续线性算子的像集的性质，证明了C*－双代数中的一个平均遮历定理，得到了C*－双代数中的线性泛函是 Haar 测度的充分必要条件；利用遍历定理和这个充分必要条件探讨了C*－双代数中 Haar 浏度存在的一些充分条件。

By getting Lebesgue characteristic of integrable function of Riemann from the definition of Gather zero measure, discussing the relation between almost continuous everywhere and existent of limit, it gets the theory which is from the function integrability to the consecution and from consecution to the limit existence .i.e. the almost limit existence is equal to the almost continuous everywhere in the integrable function of Riemann. It also gets a unified condition which has a wider range than regulated function and comes to the conclusion that the function of bounded variation is the integrable function of Riemann.

通过定义零测度集给出了可积函数的特征，讨论了其几乎处处连续与极限存在的关系，从而得到了从函数可积性到连续性，从连续性到极限存在性的函数特性理论，即可积函数中极限的几乎处处存在与几乎处处连续是等价的，得出比正规函数更加宽泛的统一条件，得出了有界变差函数是可积函数的结论。

It also emphasizes that the most importantthings to us are clarifying basic theory and method of Marxism completely,estimating current historicalcondition by rule and line,making one kind of continuable system of socialist politics,economy andculture rightly.

强调当前中国重要的问题是厘清马克思主义的基本理论和基本方法，测度当下历史条件，选择一种具体的"可持续发展"的社会主义政治、经济和文化体制。

As the application, we obtain an upper bound of the Hausdorff measure for the Cartesian product set of the middle-third Cantor set with itself.

采用这种方法，本文得到三分Cantor集自乘积集的Hausdorff测度的一个上界。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。