Academic Year/course:
2017/18
453 - Degree in Mathematics
27021 - Lebesgue Integral
Syllabus Information
Academic Year:
2017/18
Subject:
27021 - Lebesgue Integral
Faculty / School:
100 - Facultad de Ciencias
Degree:
453 - Degree in Mathematics
ECTS:
6.0
Year:
4
Semester:
First semester
Subject Type:
Compulsory
Module:
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5.1. Methodological overview
Theoretical and problem sessions on the blackboard.
Use of moodle for communicating and displaying learning material.
Mentoring.
5.2. Learning tasks
Master classes on theoretical results and key problems.
Problem sessions to understand and apply the theoretical results.
Problem assignments for individual work.
Individual tutoring.
See http://www.unizar.es/analisis_matematico/docencia.html and https://moodle2.unizar.es/ for more information and resources.
5.3. Syllabus
1) Measures.
2) Measurable functions. Integration with respect to a measure.
3) Lp spaces.
4) Decomposition of measures.
5) Radon-Nikodym and Lebesgue theorems.
6) Product measure. Fubini theorem.
5.4. Course planning and calendar
Four hours weekly of master classes during the second semester.
Exam period and dates and the academic calendar is available at the Faculty of Science web page, http://ciencias.unizar.es/web/horarios.do
5.5. Bibliography and recommended resources
Bartle, Robert G. A modern theory of integration. GSM-32, Amer. Math. Soc. 2001
Bressoud, David, M. A radical approach to Lebesgue's theory of integration. Cambridge 2008
Chae, Soo Bong Lebesgue integration. Springer-Verlag 1995
Letac, G. Integration and probability. Exercises and solutions. Springer-Verlag 1995
Tao, T. An introduction to measure theory. GSM-126, Amer. Math. Soc. 2011
See http://www.unizar.es/analisis_matematico/docencia.html and https://moodle2.unizar.es/ for more information and resources.