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Measure theory [ LMAT1322 ]

3.0 crédits ECTS 22.5 h + 15.0 h 1q

Teacher(s)	Moonens Laurent ;
Language	French
Place of the course	Louvain-la-Neuve
Main themes	Borel-Sieltjes measures. Measurable functions Integrability and integrals Convergence theorems Radon-Nikodym theorem Fubini theorem Lp spaces and their dual Representation theorem of Riesz-Markov.
Aims	The objective of the course is to introduce the notion of abstract measure space and the corresponding Lebesgue integral, then to rediscover, in this new language, the convergence theorems introduced in the first analysis courses : Fatou's lemma, Lebesgue dominated convergence, etc. After this course, students will be able to use those new tools in the context of the analysis and probability courses.
Other information	Prerequisite : MAT 1221: Mathematical analysis 3
Cycle et année d'étude	> Master [120] in Statistics: General > Bachelor in Information and Communication > Bachelor in Philosophy > Bachelor in Engineering : Architecture > Bachelor in Computer Science > Bachelor in Psychology and Education: General > Bachelor in Economics and Management > Bachelor in Human and Social Sciences > Bachelor in Motor skills : General > Bachelor in Sociology and Anthropology > Bachelor in Political Sciences: General > Bachelor in Mathematics > Bachelor in Biomedicine > Bachelor in Engineering > Bachelor in Pharmacy > Bachelor in Religious Studies > Bachelor in Physics
Faculty or entity in charge	> MATH