可积函数

令X是连续半鞅，f是R上的局部可积函数。

Let X be a continuous semimartingale , f be a locally integrable function on R.

G可积函数的Lebesgue可测性

The Lebesgue Measurability of the G Integrable Function

讨论了在[a，b]上的可积函数f（x）的平均值函数的极值问题。

The problem of extremal value of mean value functionis discussed for the integrable function f ( x ) in [ a , b ]

多元Riemann可积函数的特征与完备化

Feature and perfection of Riemann integrable function

基于集值映射的非负Lebesgue可积函数的重心选择

The Barycentric Selection on Non-negative Lebesgue Integrable Function of Set-valued Map

边值Riemann可积函数的拟插值多项式逼近阶

Order of Approximation by Quasi-Interpolating Polynomials to Riemann Integrable Functions On the Boundary of a Domain

本文讨论[0,2π]上Bochner可积函数的若干性质，并在p≥1时推广平均收敛定理。

This Paper discusses the properties of functions which are Bochner integrable on [ 0,2 π ] and extends the mean convergence theorem .

在H∞控制理论及应用其理论进行设计中，经常用到结论：在虚轴上定义的平方可积函数分别与在开左、右半平面解析且一致平方可积函数的相互对应关系。

In H-infinity control theory and control system design with the theory , the quadratic integration function defined on imaginary axis is often decomposed into analytic functions on right half-plane and left half-plane respectively .

加权P方可积函数空间Lρ~p[a，b]（p≥1）中强收敛与可数基

On the Strongly Convergence and Countable Base of the Integrable Function Space L_p ~ p [ a , b ] ( p ≥ 1 ) in the Weighted P Power

Bochner可积函数空间上线性算子的积分表示

The Representation of the Linear Operator on the Space of Bochner Integrable Functions

用初等的方法证明了[a，b]上的Riemann可积函数的连续点在[a，b]上是稠密的。

By using an elementary method , it is shown that the set of continuity points of a Riemann integrable function in is dense in .

[0,2π]上Bochner可积函数和平均收敛定理

The Functions Which Are Bochner Integrable on [ 0,2 π ] and the Mean Convergence Theorem

本文研究两个Banach空间X、Y的直和空间上凸映射的性质，其中X、Y为可积函数空间或本质有界函数空间。

In this paper , we investigate the property of convex maps defined on the directed sum of two Banach spaces X and Y , where X , Y are spaces of integrable functions or essential bounded functions .

引进函数f（x）在[a，b]上Aφ积分的概念，得到Aφ积分的若干性质，把Riemann可积函数类推广到更广泛的Aφ可积函数类。

Introducing the concept of A_ φ integral of the function f ( x ) on , some properties of A_ φ integral are obtained . The Riemann integrable functions are extended to the A_ φ integrable functions .

关于Reimann可积函数的间断点

About Discontinuity Point of Reimann Integrable Function

在研究Bochner可积函数空间上线性算子的积分表示时，一般总要求函数值域空间X具有Radon-Nikodym性质。

In studying representation of linear operator on the space of Bochner integra-ble functions by integral , authors , usually , demand that the range space X have the Radon-Nikodym property .

电磁问题数值求解中有限区间上平方可积函数空间小波基的构造

Constructions of the Wavelet Bases for the Numerical Solutions to Electromagnetic Problems

平方可积函数解析分解的构造性证明

Constructive proof about quadratic integrable function decomposition into analytic function

可积函数的原函数的存在性问题

The Existence of Primitive Function of Integrable Function Problems

有限区间上广义可积函数列逐项积分的条件

Conditions of Term by Term Integration Sequence of Integrable functions on Finite Interval

对可积函数列的有关概念和定理的推广

The Extension of the Relevant Conceptions and Theorems of the Integrable Function Column

可积函数的逼近性质的证明及其应用

The Proof and Application to Integrable Function Approximation Quality

可积函数空间上两种收敛性的关系

The relationship between two convergences in integrable function space ON THE σ - PRODUCTS

本文建立了两类可积函数的积分第一中值定理的推广形式，推广了已有结论。

Two kinds of generalizations of the first mean value theorem of integral for integrable functions with different properties are established in the paper , the results extend the previous conclusions .

用构造性的方法证明对任何定义在多维欧氏空间紧集上的勒贝格可积函数以及它的导数可以用一个单隐层的神经网络同时逼近。

It is shown in this paper by a constructive method that for any Lebesgue integrable functions defined on a compact set in a multidimensional Euclidian space , the function and its derivatives can be simultaneously approximated by a neural network with one hidden layer .

分段函数、函数的可积性与原函数存在性

Piecewise Function , Integrability and Existence of Primitive Function

本文结合实例，从几个不同的方面，给出了函数可积性与原函数存在性的关系，并得到了几个有用的结论。

The paper reveals the integrability and existence of primitive function by some examples , and it leads to some useful conclusions .

对拟完全可积共振或部分可积系统，Lyapunov函数取为系统的独立对合首次积分的最优线性组合。

For quasi-integrable and resonant Hamilton systems and quasi-partially-integrable Hamiltonian systems , the optima linear combination of the independent first integrals in involution is taken as the Lyapunov function .

本文证明了在一致可积的条件下可对Henstock可积函数列逐项积分；

This paper proves that under the condition on uniformly integrability the sequence of real & valued functions may be integrated term by term .