Week 
Topics 
Homework 
1: Feb 1620 
Review of real numbers, continuous functions, sequence of functions 
8, 11, 13, 18 p. 38 
2: Feb 2327 
Elementary Set Theory : Open , Closed, Sigma algebra, Borel sets 
27, 28, 36 p 46
43, 47 p 50 
3: Mar 0105 and 
Lebesgue Measure : Outer measure, Measurable sets, Measurable functions 

4: Mar 712 
Almost everywhere notion, Egoroff's theorem , Riemann Integrals : Darboux sums 
5,8 p 58
10, 11, 12 p 64 
5: Mar 1519 
Riemann Characterization theorem , Integrable functions, defects of Riemann integration 

6: Mar 2226 
The Lebesgue Integrals : Integral of bounded functions, Bdd convergence theorem,
Integral of nonnegative function 

7: March 29April 02 
Fatou's lemma, MCT General Lebesgue Integration, Dominated conv. Theorem 
3, 6, 7, 8 p 89
10, 13, 14, 16 p93 
8: April 0509 
Conergence in measure, Relations between different types of convergence 

9: April 1923 
Differentiation : Monotone functions, Bounded Variation functions, 

10: April 2630 
Bounded Variation functions,
Total variation Absolute continuity 
9, 10 p 104
11, 12, 20 p 111. 
11: May 0307 
The L p Spaces : Review of functional analysis, Definitions, Norms 

12: May 1014 
Completeness, Minkowski's inequality, Holder's inequality, Approximation and density 

13: May 1721 
Bounded linear functionals, Riesz Representation theorem 
8 p 123
10, 16, 17 p 127 
14: May 2428 
The Abstract Measure and Integration : Measurable spaces, measure spaces 

15: June 3104 
Measurable functions, Integration, Signed measures, The RadonNikodym theorem 
TBA 