Lecture 
Date 
What was
covered 
Notes 
Textbook Section 
1 
Jan.25 
Review L^1 space and measure theory on R (I) 

4.4 
2 
Jan.30 
Review L^1 space and measure theory on R(II) 
Get HW1 
4.4 
3 
Feb. 1 
Littlewood's 3 principles: Measurable sets, Lusin Theorem, Egoroff theorem 


4 
Feb. 6 
RieszMarkov Theorem (1). 
Due HW1; Get HW2 

5 
Feb. 8 
RieszMarkov (2) 


6 
Feb.13 
RieszMarkov (3) 
Due HW2; Get HW3 

7 
Feb.15 
Approximations by simple and step functions 


8 
Feb.20 
Riesz representation of the dual of Lp (1) 


9 
Feb.22 
Riesz representation of the dual of Lp (2) 
Due HW3; Get HW4 

10 
Feb.27 
Differentiation of BV functions: Lebesgue theorem. (1) 


11 
Mar. 1 
Differentiation of BV functions: Lebesgue theorem. (2) 


12 
Mar. 6 
Differentiation of singular measures 
Due HW4; Get HW5 

13 
Mar. 8 
Differentiation of absolutely continuous measures 


14 
Mar.13 
Topological and Metric Spaces. 


15 
Mar.15 
Separation axioms for topological spaces. The case of metric spaces. 
Due HW5 

 
Fri., Mar.16 
REVIEW SESSION 
11:00am1:00pm 
CSIC 4122 
 
Mar.1923 
SPRING BREAK 

NO CLASSES 
16 
Mar.27 
MID TERM EXAM 


17 
Mar.29 
 

NO CLASS 
18 
Apr. 3 
Normal spaces. Urysohn's Lemma 


19 
Apr. 5 
Urysohn's Metrizability Theorem 
Due HW6 

20 
Apr.10 
Compact topological spaces. Product topology. 


21 
Apr.12 
Tychonoff's Theorem 


22 
Apr.17 
Compact Metric Spaces 


23 
Apr.19 
Partition of Unity. Premeasures. 
Due HW7 

24 
Apr.24 
Measurable spaces and Spaces with measure. Preliminary results 


25 
Apr.26 
Outer Measures 


26 
May 1 
Caratheodory measurable sets. CaratheodoryHahn theorem. 


27 
May 3 
Extension results. 


28 
May 8 
Integration of simple functions 


29 
May 10 
Integration in abstract spaces with measures. Miscellaneous results. 

LAST CLASS 
 
Fri., May 11 
REVIEW SESSION 
11:00pm1:00pm 
CSIC 4122 
 
Sat., May 12 
FINAL EXAM 
CSIC 4122 
8:00am10:00am 