## 2015-06-24

### 實變函數論(一)--吳培元 / 交大

# 播放清單 (請按影片的右上角選取)

source: nctuocw    Last updated on 2013年12月9日

This is the course designed to acquaint the graduate students in the applied mathematics department with basic ideas and tools in modern analysis. This comprises the subjects of real analysis and functional analysis, the analysis developed in the 20th century and after. We will treat real analysis mainly in the first semester and functional analysis in the second. Hopefully, we can lay down a solid foundation for further usage in some other theoretical or applied area. After taking the course, the students are expected to have the general idea on the modern ways to attack the analysis problems.

Lec04 實變函數論(一) Class4 Sec.1.4. Constructing outer measure 48:12
Lec08 實變函數論(一) Class8 Sec.1.9 Construction of metric outer measure 49:32
Lec05 實變函數論(一) Class5 Sec.1.5-1.6 Lebesgue measure 1:36:05
Lec29 實變函數論(一) Class29 48:20
Lec07 實變函數論(一) Class7 Sec.1.8-1.9 Construction of metric outer meas 1:34:00
Lec26 實變函數論(一) Class26 Sec. 2.13. Lebesgue decomposition 1:31:46
Lec28 實變函數論(一) Class28 Sec. 2.14 Fundamental Thm of Calculus on 1:36:11
Lec33 實變函數論(一) Class33 42:53
Lec09 實變函數論(一) Class9 Sec.1.10 Signed measure 1:37:22
Lec06 實變函數論(一) Class6 Sec.1.7 Metric space 48:06
Lec30 實變函數論(一) Class30 1:37:42
Lec27 實變函數論(一) Class27 Sec. 2.13. Lebesgue decomposition 53:01
Lec14 實變函數論(一) Class14 Sec 2.4 Convergence in measure 54:59
Lec12 實變函數論(一) Class12 Sec 2.3. Egoroffs Thm. 47:01
Lec13 實變函數論(一) Class13 Sec 2.3 Egoroffs Thm. 1:22:24
Lec25 實變函數論(一) Class25 47:23
Lec31 實變函數論(一) Class31 48:12
Lec01 實變函數論(一) Class1  Measure theory 17:18
Lec02 實變函數論(一) Class2 49:59
Lec11 實變函數論(一) Class11  Integration 1:34:33
Lec10 實變函數論(一) Class10 47:21
Lec03 實變函數論(一) Class3 Sec.1.2. Measure  Sec.1.3. Outer Me 1:44:19
Lec24 實變函數論(一) Class24 1:34:22
Lec15 實變函數論(一) Class15 Sec 2.5 Integrals of simple functions 1:41:14
Lec23 實變函數論(一) Class23 Sec 2.11 (Proper) Riemann integral 50:05
Lec32 實變函數論(一) Class32 1:35:36
Lec22 實變函數論(一) Class22 Sec. 2.10 Applications of DCT 1:33:59
Lec16 實變函數論(一) Class16 Sec. 2.6 Integrable functions 46:37
Lec17 實變函數論(一) Class17 1:26:21
Lec18 實變函數論(一) Class18 Sec. 2.7 Properties of integral 47:39
Lec21 實變函數論(一) Class21 Sec.2.9 DCT 50:00
Lec20 實變函數論(一) Class20 1:33:07
Lec19 實變函數論(一) Class19 48:25