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 ,

__Week(2):____ __Elementary
properties of a measure , finite measure and

Measure , complete measure.

** Week(3):** Measurable functions and their properties .

** Week(4+5):** Integration respect to measure

** 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

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 .