测度

By getting Lebesgue characteristic of integrable function of Riemann from the definition of gather zero measure, it discusses the relation between almost continuous everywhere and existent of limit, and gets that the almost continuous everywhere is equal to the almost limit existence everywhere in 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，即可积函数中几乎处处连续与极限的几乎处处存在是等价的，得出了比正规函数更加广泛的统一条件，得出了有界变差函数是可积函数的结论。

Similarly, we discuss the relation between fundamental convergence in fuzzy measure and fuzzy mean fundamental convergence of fuzzy integrals.

类似地，还讨论了"依测度基本"与"广义模糊积分平均基本"的关系。

In chapter 3, we study the relation between convergence in fuzzy measure of nonnegative fuzzy measurable functions and fuzzy mean convergence of fuzzy integrals.

研究了非负模糊可测函数列依测度收敛与广义模糊积分平均收敛之间的关系。

On the other hand, we also give several terse sufficiency conditions where the fuzzy mean convergence of fuzzy integrals implies the convergence in fuzzy measure and making them equivalent.

另一方面，文中还给出了广义模糊积分平均收敛蕴涵依测度收敛的几个简洁的充分性条件，以及使两者等价的条件。

Furthermore, as its corollary, we still get several terse and pragmatic sufficiency conditions where the convergence in fuzzy measure implies the fuzzy mean convergence of fuzzy integrals.

作为这一结果的推论，还得到了依测度收敛蕴涵广义模糊积分平均收敛的几个简洁、实用的充分性条件。

First, we present various new convergence concepts for sequence of fuzzy random variables, including convergence sure, convergence almost sure, uniform convergence, uniform convergence almost sure, almost uniform convergence, convergence in chance measure, and their corresponding weak convergence. Second, the relations among some types of convergence are studied. Finally, we design some algorithms about fuzzy random simulations to compute the mean chance of fuzzy random event, find the optimistic value of a return function, and evaluate the expected value of a fuzzy random variable.

首先，提出了几类模糊随机变量序列的收敛性概念，包括：必然收敛、几乎必然收敛、一致收敛、几乎必然一致收敛、近一致收敛、依机会测度收敛以及与以上概念相对应的弱收敛；其次，讨论了收敛性之间的关系；最后我们设计了模糊随机模拟算法，用于计算模糊随机事件的平均机会，寻找收益函数的乐观值，以及估计模糊随机变量的期望值。

Properties of measurable functions; approximation by simple functions and by continuous functions; convergence in measure; Egoroff's theorem; Lusin's theorem; Jensen's inequality.

可测函数。可测函数的性质；简单和连续函数逼近；测度收敛；叶果洛夫定理；鲁津定理；詹森不等式

First, we present various new convergence concepts for sequence of fuzzy random variables, including convergence sure, convergence almost sure, uniform convergence, uniform convergence almost sure, almost uniform convergence, convergence in chance measure, and their corresponding weak convergence.

首先，提出了几类模糊随机变量序列的收敛性概念，包括：必然收敛、几乎必然收敛、一致收敛、几乎必然一致收敛、近一致收敛、依机会测度收敛以及与以上概念相对应的弱收敛；其次，讨论了收敛性之间的关系；最后我们设计了模糊随机模拟算法，用于计算模糊随机事件的平均机会，寻找收益函数的乐观值，以及估计模糊随机变量的期望值。

Secondly,at satisfying certain conditions, we obtain some convergence theorem,which is similar with the classical Lebesgue integral.

最后，在模糊测度空间上针对这种积分讨论了T—模糊值积分方程，获得一些重要结果。

The theory foundation of the method is given, which proves that the expectation and variance are uniformly convergent in measure space, and the orthogonal function series used to approach the sensitivity function is uniformly convergent.

文中描述了目标机动对命中误差灵敏度的拟合正交函数系及其一致收敛性，并用测度理论证明了小样本方法估算期望和方差的逼近的一致收敛性质。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。