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 ,
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 .