绝对连续测度

Theorem 1 constructs a set of universal measure zero using continuous extension; Theorem 2 verifies absolutely continuous function being of good property under some condition; Theorem 3 reveals some relation between real function and meager.

定理1 主要运用了连续延拓构造了一个泛测度零集；定理2 证明绝对连续函数在一定条件下具有良好的性质；定理3 揭示了实函数与第一纲集的某种关系。

It is proved that if μ is not singular, then it is absolutely continuous with respect to Lebesgue measure.

本文证明了μ要么关于Lebesgue测度奇异，要么关于Lebesgue测度绝对连续。

Let μ be a smooth measure with a quasi regular Dirichlet form, A μ be its non negative additive functional,and U α A μ be the α Potential operator of A μ.

设μ是拟正则狄氏型的光滑测度，Aμ是其对应的非负连续可加泛函，UαAμ是Aμ的α位势算子，本文证明了测度μUαAμ关于μ的绝对连续性，并以R－N导数dμUαAμdμ刻划了μ具有有限能量积分的条件。

Firstly, we investigate the Dirichlet problems comparison principle on a bounded subset for this fully nonlinear intergro-differential equation, at the same time we must assume the measure in the intergro-differential item is absolute continuous.

首先研究这类完全非线性积分微分方程在有界区域上Dirichlet问题的比较原理，此时须假设积分项所涉及的测度是绝对连续的。

After introducing some basic results from ergodic theory, two probIems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system.

首先介绍了遍历理论的一些经典结果；然后着重研究了对应于混沌映射的绝对连续不变测度的存在性与计算问题，这归结于相应的Frobenius-Perron算子的泛函分析与数值分析；最后《确定性系统的统计性质》介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些最新应用。

Jiu Ding,Aihui Zhou,Statistical Properties of Deterministic Systems Statistical Properties of Deterministic Systems discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two probIems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation.

摘要本书介绍的是确定性离散动力系统统计性质的基本理论与计算方法，首先介绍了遍历理论的一些经典结果；然后着重研究了对应于混沌映射的绝对连续不变测度的存在性与计算问题，这归结于相应的Frobenius—Perron算子的泛函分析与数值分析；最后本书介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些最新应用。

If 〓 is an absolutely continuousmeasure and is represented by a measurable function f on Q,then u is said tobe the generalized solution of(1),and 〓 to be the parabolic Monge-Amperemeasure.

定义1由legendre变换定义了一个Q上的测度〓（4）其中〓为〓空间中的Lebesgue测度，若〓是一个绝对连续测度且在Q上由可测函数〓表示，则称u为方程（1）的广义解、称测度〓为抛物型Monge-Ampère测度。

New properties and improvements on VSI. Combining the density processof local absolute continuous measure, properties of the martingale space H1 and semi-martingale space, and the closed image theorem of functional analysis (see the proofs ofTheorem 2.4.5 and Theorem 2.4.10), we obtain the general form of Girsanov Theorem forsemi-martingale vector stochastic integral .

特别是利用局部绝对连续测度的密度过程、鞅空间H1与半鞅空间的性质以及泛函分析中的闭图像定理(见定理2.4.5与定理2.4.10的证明)获得了一般形式的半鞅向(来源：Ab6BC论a1文网www.abclunwen.com)量随机积分的Girsa-nov定理，它对于随机分析的理论与随机积分的应用都具有重要价值。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。