SF2709 Integration Theory, 7.5 hp
Fall term 2008

        Last news

• Program of the oral examination  
  
• No homework assignement to 9 December!
       
  
• The homework assignement to 2 December:
  Section 4.4: 1, 4
  
       
  
• The homework assignement to 25 November:
  Section 4.2: 3, 4, 9;
  Section 4.3: 3.
       
  
• The homework assignement to 18 November:
  Section 4.1: 1, 2, 3, 5.
  
       
  
• The homework assignement to 11 November:
  Section 3.3: 7, 8b, 9. Attention: in 3.3.8b you may use without proof 3.3.8a and you may assume for simplicity that $\phi$ is differentiable.
       
  
• The homework assignement to 4 November:
  Section 3.1: 1, 2, 4
  Section 3.3: 7
  
       
  
• The homework assignement to 21 Okt:
  Section 2.4: 8, 10
  Section 2.5: 4
  
       
  The homework assignement to 14 Okt:
  Section 2.3: 7
  Section 2.4: 1, 2, 3
       
  
• The homework assignement to 7 Okt:
  Section 2.3: 2, 4, 6
  Attention: 7a is excluded!
  
       
  
• The homework assignement to 30 Sep:
  Section 2.1: 1, 3, 4, 6.
       
  
• The homework assignement to 23 Sep:
  Section 1.4: 1, 2, 3, 4
  
       
  
• The homework assignement to 16 Sep:
  Section 1.3: 1a, 2,3,7
  
       
  
• The homework assignement to 9 Sep:
  Section 1.1: 1,2,4,6.    Section 1.2: 1ab, 2,4.
       
  

        Course information

• Course leader: Serguei Shimorin, 08-790 6692,   shimorin@math.kth.se
   
• Schedule: The course holds during the fall term 2008 once per week on Tuesdays at 13.15 - 15.00 in the room 3733 at the Department of Mathematics.
  The course is given in English.
   
• Prerequisites: Analys grundkurs SF2700.
   
• Course description: The course goal is to learn about the notions of measure and Lebesgue integral. Emphasis will be on the Lebesgue measure and integral on the real line and Euclidian spaces.
   
• Topics
  
  Riemann integral
  Lebesgue measure, measurable functions. Egoroff's theorem.
  Signed measures, Jordan decomposition, absolutely continuous and singular measures, Radon-Nykodim theorem, Lebesgue decomposition.
  Absolutely continuous functions, functions of bounded variation, Fubini's theorem. Lp spaces.
  Hölder ad Minkowski inequalities. Normed and metric spaces.
   
• Course litterature
  
  
  • Donald L. Cohn, Measure Theory. Birkhäuser; Boston, Basel, Berlin.
  
   
• Examination: The examination consists of two parts: homework assignements during the course and an oral test at the end. The homework assignements are given after each lecture for a week and they should be delivered to the lecturer at the next lecture for grading. To pass the course it is sufficient (and necessary!) to have 50% accepted homework exercises. This gives the grade "E". More than 80% accepted exercises gives the grade "D". To get higher grade ("C", "B" or "A") one should pass also the oral test and the final grade will depend on it and the number of accepted homework exercises.
   
  

        Lecture plan (preliminary)