Syllabus

                       M-580          MEASURE  THEORY

      1)Department of Mathematics , Faculty of Sciences .

      2)Teaching by : Prof.Moustafa DAMLAKHI

      3)Credit hours 4 (4+0)

      4) Higher study  (M.Sc.cours)

      5) First Semester , 1429/1430 H .

Week(1) :  Ring, algebra , -algebra , measure space and its properties .

Week(2): Elementary properties of a measure , finite measure  and -finite

Measure , complete measure.

Week(3): Measurable functions and their properties .

Week(4+5): Integration respect to measure  defined on a , where is a measure space .Integration of a simple non- negative functions, Integration of a non- negative measurable functions , Integration of a measurable functions and some properties  of integrable fuctions

Week(6): The theorems of convergence : Fatou 's Lemma , Lebesgue 's Monotone convergence theorem, Lebesgue 's Dominated convergence theorem.

Completion of a measure .

Week(7) : The Rodon-Nikodym  Theorem and its applications .

Week(8+9): Measure and outer measure , some properties of outer measure and approximation theorem .

Week(10+11): Measure and integration in product space , product measure and

Fubini 's Theorem.

Week(12): , Lebesgue's –Stieltjes integration .

Week(13+14): Inequalities and  - spaces and Bounded Linear functional on  .

 

The Distribution of Marks :

1)   25 marks for the homework .

2)   25 marks for the Mid-term

3)   50 marks for the final Exam .

The Mid-Term Exam will be 23/12/1429 H (21/12/2008)

From 8 to 10 am .