SF2709 Integration Theory, 7.5 hp
Fall term 2009

        Last news

• Program of the oral examination  
  
   
  
• Homework assignement to 3 Dec:
  4.4: 1,4.
   
  
• Homework assignement to 26 Nov:
  4.2: 3,4,9;
  4.3: 3.
   
  
• Homework assignement to 19 Nov:
  4.1: 1,2,3.
   
  
• Homework assignement to 12 Nov:
  3.3: 7, 8b, 9. In exercise 3.3.8b) you may assume for simplicity that the function $\phi$ is differentiable.
   
  
• Homework assignement to 5 Nov:
  3.1: 1, 2, 4.
• Homework assignement to 29 Okt:
  2.4: 8, 10;
  2.5: 4.
• Homework assignement to 15 Okt:
  2.3: 7
  2.4: 1, 2, 3.
• Homework assignement to 8 Okt:
  2.3: 4, 6.
• Homework assignement to 1 Okt:
  1.4: 3, 4;
  2.1: 1, 3, 4.
• Homework assignement to 24 Sep:
  1.4: 1, 2.
• Homework assignement to 17 Sep:
  1.3: 1a, 2, 3, 7.
  Solution of exercise 1.3.7
• Homework assignement to 10 Sep:
  1.1: 1,2,4,6 and 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 2009 once per week on Thursdays at 13.15 - 15.00 in the room 3733 at the Department of Mathematics. Attention: there is no lecture 22 Oktober.
  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
  
  Abstract measures. Measurable functions. Lebesgue integration.
  Lebesgue measure. Functions of bounded variation
  Signed measures, Jordan decomposition, absolutely continuous and singular measures, Radon-Nykodim theorem, Lebesgue decomposition.
  Fubini's theorem.
  Normed and metric spaces. Lp spaces. Hölder ad Minkowski inequalities.
   
• 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.
  For graduate students it is sufficient to have 50% accepted homework exercises to pass the course.
   
  

        Lecture plan (preliminary)