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ShowBL > 【中文配音+人工矫正】印度科学研究所IISc-测度论｜勒贝格积分·L^p空间｜E K Narayanan｜Measure Theory 2020

【中文配音+人工矫正】印度科学研究所IISc-测度论｜勒贝格积分·L^p空间｜E K Narayanan｜Measure Theory 2020 - [必看] 1分钟：双语怎么切-充电解锁课程站

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[中文] 00 课程导引

[中文] 00 课程导引
[英文] 00 Intro Measure Theory｜完整英文原声在后半部

[英文] 00 Intro Measure Theory｜完整英文原声在后半部
[必看] 1分钟：双语怎么切-充电解锁课程站

[必看] 1分钟：双语怎么切-充电解锁课程站
[中文] 01 黎曼积分回顾与σ代数引入

[中文] 01 黎曼积分回顾与σ代数引入
[中文] 02 σ代数与可测性

[中文] 02 σ代数与可测性
[中文] 03 可测函数与简单函数逼近

[中文] 03 可测函数与简单函数逼近
[中文] 04 可数可加测度的性质

[中文] 04 可数可加测度的性质
[中文] 05 正可测函数的积分

[中文] 05 正可测函数的积分
[中文] 06 正简单函数积分的性质

[中文] 06 正简单函数积分的性质
[中文] 07 单调收敛定理与Fatou引理

[中文] 07 单调收敛定理与Fatou引理
[中文] 08 复值可测函数的积分

[中文] 08 复值可测函数的积分
[中文] 09 控制收敛定理

[中文] 09 控制收敛定理
[中文] 10 零测集与完备化

[中文] 10 零测集与完备化
[中文] 11 MCT、Fatou引理与DCT的推论

[中文] 11 MCT、Fatou引理与DCT的推论
[中文] 12 R^n中的矩形及其性质

[中文] 12 R^n中的矩形及其性质
[中文] 13 R^n上的外测度

[中文] 13 R^n上的外测度
[中文] 14 R^n上外测度的性质

[中文] 14 R^n上外测度的性质
[中文] 15 勒贝格可测集与勒贝格测度

[中文] 15 勒贝格可测集与勒贝格测度
[中文] 16 勒贝格σ代数

[中文] 16 勒贝格σ代数
[中文] 17 勒贝格测度

[中文] 17 勒贝格测度
[中文] 18 可测集的精细性质

[中文] 18 可测集的精细性质
[中文] 19 勒贝格测度的不变性

[中文] 19 勒贝格测度的不变性
[中文] 20 不可测集

[中文] 20 不可测集
[中文] 21 可测函数

[中文] 21 可测函数
[中文] 22 黎曼积分与勒贝格积分

[中文] 22 黎曼积分与勒贝格积分
[中文] 23 局部紧Hausdorff空间

[中文] 23 局部紧Hausdorff空间
[中文] 24 Riesz表示定理

[中文] 24 Riesz表示定理
[中文] 25 正Borel测度

[中文] 25 正Borel测度
[中文] 26 由Riesz表示定理得到勒贝格测度

[中文] 26 由Riesz表示定理得到勒贝格测度
[中文] 27 勒贝格测度的构造

[中文] 27 勒贝格测度的构造
[中文] 28 勒贝格测度的不变性（续）

[中文] 28 勒贝格测度的不变性（续）
[中文] 29 线性变换与勒贝格测度

[中文] 29 线性变换与勒贝格测度
[中文] 30 Cantor集

[中文] 30 Cantor集
[中文] 31 Cantor函数

[中文] 31 Cantor函数
[中文] 32 非Borel的勒贝格集

[中文] 32 非Borel的勒贝格集
[中文] 33 L^p空间

[中文] 33 L^p空间
[中文] 34 L^p范数

[中文] 34 L^p范数
[中文] 35 L^p的完备性

[中文] 35 L^p的完备性
[中文] 36 L^p空间的性质

[中文] 36 L^p空间的性质
[中文] 37 L^p空间的例子

[中文] 37 L^p空间的例子
[中文] 38 乘积σ代数

[中文] 38 乘积σ代数
[中文] 39 乘积测度（一）

[中文] 39 乘积测度（一）
[中文] 40 乘积测度（二）

[中文] 40 乘积测度（二）
[中文] 41 Fubini定理（一）

[中文] 41 Fubini定理（一）
[中文] 42 Fubini定理（二）

[中文] 42 Fubini定理（二）
[中文] 43 乘积测度的完备化

[中文] 43 乘积测度的完备化
[中文] 44 极坐标

[中文] 44 极坐标
[中文] 45 Fubini定理的应用

[中文] 45 Fubini定理的应用
[中文] 46 复测度（一）

[中文] 46 复测度（一）
[中文] 47 复测度（二）

[中文] 47 复测度（二）
[中文] 48 绝对连续测度

[中文] 48 绝对连续测度
[中文] 49 L^2空间

[中文] 49 L^2空间
[中文] 50 连续线性泛函

[中文] 50 连续线性泛函
[中文] 51 Radon-Nikodym定理（一）

[中文] 51 Radon-Nikodym定理（一）
[中文] 52 Radon-Nikodym定理（二）

[中文] 52 Radon-Nikodym定理（二）
[中文] 53 Radon-Nikodym定理的推论（一）

[中文] 53 Radon-Nikodym定理的推论（一）
[中文] 54 Radon-Nikodym定理的推论（二）

[中文] 54 Radon-Nikodym定理的推论（二）
[中文] 55 L^p空间上的连续线性泛函（一）

[中文] 55 L^p空间上的连续线性泛函（一）
[中文] 56 L^p空间上的连续线性泛函（二）

[中文] 56 L^p空间上的连续线性泛函（二）
[中文] 57 Riesz表示定理（一）

[中文] 57 Riesz表示定理（一）
[中文] 58 Riesz表示定理（二）

[中文] 58 Riesz表示定理（二）
[中文] 59 Hardy-Littlewood极大函数

[中文] 59 Hardy-Littlewood极大函数
[中文] 60 勒贝格微分定理

[中文] 60 勒贝格微分定理
[中文] 61 绝对连续函数（一）

[中文] 61 绝对连续函数（一）
[中文] 62 绝对连续函数（二）

[中文] 62 绝对连续函数（二）
[英文] 01 Review of Riemann integration and introduction to sigma algebras

[英文] 01 Review of Riemann integration and introduction to sigma algebras
[英文] 02 Sigma algebras and measurability

[英文] 02 Sigma algebras and measurability
[英文] 03 Measurable functions and approximation by simple functions

[英文] 03 Measurable functions and approximation by simple functions
[英文] 04 Properties of countably additive measures

[英文] 04 Properties of countably additive measures
[英文] 05 Integration of positive measurable functions

[英文] 05 Integration of positive measurable functions
[英文] 06 Some properties of integrals of positive simple functions

[英文] 06 Some properties of integrals of positive simple functions
[英文] 07 Monotone convergence theorem and Fatou's lemma

[英文] 07 Monotone convergence theorem and Fatou's lemma
[英文] 08 Integration of complex valued measurable functions

[英文] 08 Integration of complex valued measurable functions
[英文] 09 Dominated convergence theorem

[英文] 09 Dominated convergence theorem
[英文] 10 Sets of measure zero and completion

[英文] 10 Sets of measure zero and completion
[英文] 11 Consequences of MCT, Fatou's lemma and DCT

[英文] 11 Consequences of MCT, Fatou's lemma and DCT
[英文] 12 Rectangles in R^n and some properties

[英文] 12 Rectangles in R^n and some properties
[英文] 13 Outer measure on R^n

[英文] 13 Outer measure on R^n
[英文] 14 Properties of outer measure on R^n

[英文] 14 Properties of outer measure on R^n
[英文] 15 Lebesgue measurable sets and Lebesgue measure on R^n

[英文] 15 Lebesgue measurable sets and Lebesgue measure on R^n
[英文] 16 Lebesgue sigma algebra

[英文] 16 Lebesgue sigma algebra
[英文] 17 Lebesgue measure

[英文] 17 Lebesgue measure
[英文] 18 Fine properties of measurable sets

[英文] 18 Fine properties of measurable sets
[英文] 19 Invariance properties of Lebesgue measure

[英文] 19 Invariance properties of Lebesgue measure
[英文] 20 Non measurable set

[英文] 20 Non measurable set
[英文] 21 Measurable functions

[英文] 21 Measurable functions
[英文] 22 Riemann and Lebesgue integrals

[英文] 22 Riemann and Lebesgue integrals
[英文] 23 Locally compact Hausdorff spaces

[英文] 23 Locally compact Hausdorff spaces
[英文] 24 Riesz representation theorem

[英文] 24 Riesz representation theorem
[英文] 25 Positive Borel measures

[英文] 25 Positive Borel measures
[英文] 26 Lebesgue measure via Riesz representation theorem

[英文] 26 Lebesgue measure via Riesz representation theorem
[英文] 27 Construction of Lebesgue measure

[英文] 27 Construction of Lebesgue measure
[英文] 28 Invariance properties of Lebesgue measure

[英文] 28 Invariance properties of Lebesgue measure
[英文] 29 Linear transformations and Lebesgue measure

[英文] 29 Linear transformations and Lebesgue measure
[英文] 30 Cantor set

[英文] 30 Cantor set
[英文] 31 Cantor function

[英文] 31 Cantor function
[英文] 32 Lebesgue set which is not Borel

[英文] 32 Lebesgue set which is not Borel
[英文] 33 L^p spaces

[英文] 33 L^p spaces
[英文] 34 L^p norm

[英文] 34 L^p norm
[英文] 35 Completeness of L^p

[英文] 35 Completeness of L^p
[英文] 36 Properties of L^p spaces

[英文] 36 Properties of L^p spaces
[英文] 37 Examples of L^p spaces

[英文] 37 Examples of L^p spaces
[英文] 38 Product sigma algebra

[英文] 38 Product sigma algebra
[英文] 39 Product measures I

[英文] 39 Product measures I
[英文] 40 Product measures II

[英文] 40 Product measures II
[英文] 41 Fubini's theorem I

[英文] 41 Fubini's theorem I
[英文] 42 Fubini's theorem II

[英文] 42 Fubini's theorem II
[英文] 43 Completeness of product measures

[英文] 43 Completeness of product measures
[英文] 44 Polar coordinates

[英文] 44 Polar coordinates
[英文] 45 Applications of Fubini's theorem

[英文] 45 Applications of Fubini's theorem
[英文] 46 Complex measures I

[英文] 46 Complex measures I
[英文] 47 Complex measures II

[英文] 47 Complex measures II
[英文] 48 Absolutely continuous measures

[英文] 48 Absolutely continuous measures
[英文] 49 L^2 space

[英文] 49 L^2 space
[英文] 50 Continuous linear functionals

[英文] 50 Continuous linear functionals
[英文] 51 Radon Nikodym theorem I

[英文] 51 Radon Nikodym theorem I
[英文] 52 Radon Nikodym theorem II

[英文] 52 Radon Nikodym theorem II
[英文] 53 Consequences of Radon Nikodym theorem I

[英文] 53 Consequences of Radon Nikodym theorem I
[英文] 54 Consequences of Radon Nikodym theorem II

[英文] 54 Consequences of Radon Nikodym theorem II
[英文] 55 Continuous linear functionals on L^p spaces I

[英文] 55 Continuous linear functionals on L^p spaces I
[英文] 56 Continuous linear functionals on L^p spaces II

[英文] 56 Continuous linear functionals on L^p spaces II
[英文] 57 Riesz representation theorem I

[英文] 57 Riesz representation theorem I
[英文] 58 Riesz representation theorem II

[英文] 58 Riesz representation theorem II
[英文] 59 Hardy Littlewood maximal function

[英文] 59 Hardy Littlewood maximal function
[英文] 60 Lebesgue differentiation theorem

[英文] 60 Lebesgue differentiation theorem
[英文] 61 Absolutely continuous functions I

[英文] 61 Absolutely continuous functions I
[英文] 62 Absolutely continuous functions II

[英文] 62 Absolutely continuous functions II