Oct 17, 2019   2:23 a.m. Hedviga
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Course syllabus D1-TMI - Measure and integral theory (FCE - 2019/2020 - post-graduate studies)


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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Civil Engineering
Course unit code: D1-TMI
Course unit title: Measure and integral theory
Mode of delivery, planned learning activities and teaching methods:
workshop2 hours weekly / 26 hours per semester of study (on-site method)

 
Credits allocated: 5
 
Recommended semester/trimester: Applied Mathematics - doctoral (semi-compulsory), 1. year
Applied Mathematics (in english language) - doctoral (semi-compulsory), 1. year
Level of study: 3.
Prerequisites for registration: none
 
Assesment methods:
test during the semester, exam
 
Learning outcomes of the course unit:
Non-additive modelling of uncertainty and applications are a basic aim of this subject. It brings also an overview of various types of monotone measures and integrals, including their properties, and identification methods when considering real data.
 
Course contents:
- Probability measures and some deduced set functions
- Fuzzy measures, decomposable measures
- Interaction modelling, Möbius transform
- General approach to integration
- Choquet and Sugeno integrals
- Some other kinds of real-valued integrals
 
Recommended or required reading:
Basic:
WANG, Z. -- KLIR, G J. Generalized Measure Theory. New York : Springer Science+Business Media, LLC, 2009. 381 p. ISBN 978-0-387-76851-9.
DENNEBERG, D. Non-additive measure and integral. Dordrecht: Kluwer Academic Publishers, 1994.
PAP, E. Null-Additive set functions. Bratislava : Ister Science, 1995. 315 p. ISBN 80-88683-12-2.
PAP, E. Handbook of measure theory I, II. Amsterdam: North Holland/Elsevier Science, 2002.

 
Language of instruction: slovak and english
 
Notes:
 
Courses evaluation:
Assessed students in total: 7

PN
100,0 %0 %
Name of lecturer(s): prof. RNDr. Radko Mesiar, DrSc. (examiner, instructor, lecturer, person responsible for course, tutor) - slovak, english
Ing. Peter Sarkoci, PhD. (examiner, instructor, lecturer) - slovak
 
Last modification: 31. 10. 2017
Supervisor: prof. RNDr. Radko Mesiar, DrSc. and programme supervisor


Last modification made by Ing. Peter Korčák on 10/31/2017.

Type of output: