Department of Mathematics

Lecturer	Salim HAMAMDIA
Information	Bachelor - Mathematics Department of Mathematics Website : https://www.univ-soukahras.dz/en/module/492 Semester : S5 Unit : UEF5.1 Credit : 6 Coefficient: 4
Content	Chapter 1: Sets and Measures Review of set theory Algebras and tribes Positive measures, probability Properties of measures, outer measures, complete measures The Lebesgue measure on the Borel tribe Chapter 2: Measurable Functions, Random Variables Step functions Measurable functions and random variables Characterization of measurability Convergence almost everywhere and convergence in measure Chapter 3: Integrable Functions Integral of a positive step function Integral of a positive measurable function Integral of a measurable function Comparison of the Lebesgue integral with the Riemann integral Measure and probability density Monotone convergence and Fatou\\\'s lemma The space L p of integrable functions Dominated convergence theorem in L p Continuity and differentiability under the sum sign Chapter 4: Product of Measure Spaces Product measure, definition Fubini\\\'s theorem and consequences
Evaluation	Exam: 60% Directed activities: 40% Evaluation method: Mini quiz: 12 points Participation: 3 points Discipline: 2 points Homework: 3 points