控制收敛定理

我们首先得到Φ（u，w）的瑕疵离散更新方程，利用控制收敛定理得出Φ（0，w）的显式解；

At first , we obtain the defective discrete renewal equation of expected discounted penalty . The exact solution of Φ( 0 ,ω) is obtained by applying dominated convergence theorem .

其次，证明了关于apHenstockStieltjes积分的等度可积定理，Cauchy扩张定理以及控制收敛定理。

Next , we prove the Equi integrability theorem , the Cauchy extension theorem and the dominated convergence theorem for the ap Henstock Stieltjes integral .

Lebesgue控制收敛定理的一个应用s.收敛。

Application of Lebesgue Control Convergent Theorem S_n ∈ L_1 , then S_n converges almost surely .

积分连续性定理和Lebesgue控制收敛定理的新证明

The new proofs of integral continuous theorem and Lebesgue controlled convergence theorem

（KH）积分的控制收敛定理

The control covergent theorem of ( KH ) - integration

利用Lebesgue控制收敛定理将未确知数的除法推广到二未确知数范围。

Lebesgue controlling convergence theory is used to extend the division of unascertained numbers into the area of 2 unascertained numbers .

实变函数中有几个克服了黎曼积分的缺陷的积分极限定理：控制收敛定理、Levi引理、Fatou引理。

Real variable function theory is composed of three integral limitation theorems including Control Convergence theorem , Levi Lemma , Fatou Lemma .

在研究支撑函数性质的基础上，证明了随机集列关于单调减σ域族条件期望的强下极限、弱上极限的Fatou引理及KM意义下的控制收敛定理。

Then show Fatou 's lemma in the sense of strong lower-limit , weak upper-limit , and convergence theorem in the sense of K-M for set-valued conditional expectation with monotone decrease sequence of σ - fields .

对实变函数中的几个积分极限定理进行了研究，证明了控制收敛定理、Levi引理和Fatou引理是相互等价的推断。

Three integral limit theorems , I e. , Control Convergence theorem , Levi Lemma and Fatou Lemma in real variable functions are studied and proved , which concludes that the three are equivalent actually .

第二节了研究一类具连续变量偶数阶中立型时滞差分方程，利用Lebesgue控制收敛定理给出这类方程存在最终有界正解的一个充分必要条件，得到相应新的比较定理。

In the second section , we consider the even-order neutral difference equations with continuous arguments . We use Lebesgue ' dominated convergence theorem and obtain a necessary and sufficient condition for the existence of eventually positive and bounded solutions .

通过Galerkin方法、勒贝格控制收敛定理、Gronwall不等式及广义上下解方法给出一类非线性抛物&常微弱耦合方程组混合问题广义解的单调迭代法；

Galerkin method , Lebesque control-convergent theorem , Gronwall inequality and the method of generalized upper and lower solution were employed to demonstrate the monotone iteration method generalized solution for the mixed boundary value problem of the weakly coupled parabolic and ordinary system .

在一定条件下，本文给出了无界随机集序列关于条件期望的弱上极限Fatou引理，由此还得到了无界随机集序列在K&M收敛性意义下的控制收敛定理和单调收敛定理。

Under some conditions , Fatou 's lemma for conditional expectations of the weak upper limit of unbounded random sets sequence is given in the paper . The dominated convergence theorem and monotone convergence theorem in the sense of K-M convergence are also obtained .

本文给出了集合序列弱极限的表示定理，得到了随机集列关于σ-域流的条件期望序列在弱收敛意义下的Fatou型引理和控制收敛定理。

In this paper , a representation theorem is given for the weak limit of a sequence of sets in a Banach space . We obtain Fatou 's lemmas and dominated convergence theorems for set-valued conditional expectations with an increasing sequence of σ - fields .

在可测模糊随机函数及模糊值函数积分的基础上，研究了模糊值函数的有界控制收敛定理。

This paper gives the control convergent theorem of integral for fuzzy random functions on basis fuzzy functions and fuzzy integral .

并利用Lebegue控制收敛定理，建立了具有变系数差分方程振动的充分条件。

Furthermore , sufficient conditions for oscillation of difference equations with variable coefficients are established by the aid of Lebesgue contral convergence theorem .

并给出了σ弱积分存在的条件及σ弱算子拓扑下的控制收敛定理。

And the condition of σ - weak integral 's existence is given . The Dominated Convergence Theorem under the σ - weak operator topology is also given .

研究了函数序列关于弱收敛概率测度序列积分的控制收敛性，得到了控制收敛性定理，进而研究了期望泛函序列的上图收敛性，得到了概率测度弱收敛的若干新的等价条件。

Dominated convergence theorems for the integration of function sequence with respect to weak convergence probability measure sequence are studied . And some new equivalent conditions of weak convergence of probability measure are obtained . Then a sufficient condition of the epi-convergence of expectant functional sequence is obtained .

对强可加向量测度建立了一个控制一致收敛结果，是对非负数值测度的控制一致收敛定理的一般化。

For strongly additive vector measures we establish a dominated uniform convergence result which is a generalization of a fact in the case of nonnegative scalar valued measures .