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Course, academic year 2022/2023
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Selected Topics on Measure Theory - NMTP535
Title: Vybrané partie z teorie míry
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Guarantor: prof. RNDr. Jan Rataj, CSc.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinně volitelné
Classification: Mathematics > Real and Complex Analysis
Incompatibility : NMAT010
Interchangeability : NMAT010
Is interchangeable with: NMAT010
Annotation -
Last update: T_MUUK (27.04.2016)
Selected results completing the lecture NMMA203 Measure and Integration Theory, with respect to applications in probability theory> Hausdorff measure and dimension, Lebesgue density theorem, Haar measure, disintegration theorem.
Aim of the course -
Last update: T_MUUK (27.04.2016)

To teach the students of the master studies in Probability, Mathematical Statistics and Econometrics certain approaches useful in probability theory

Course completion requirements - Czech
Last update: RNDr. Jitka Zichová, Dr. (14.06.2019)

Ústní zkouška.

Literature -
Last update: T_MUUK (27.04.2016)

Morgan F.: Geometric Measure Theory: a Beginner's Guide.Academic Press, San Diego 1988

Mattila P.: Geometry of Sets and Measures in Euclidean Spaces. Cambridge Univ. Press, Cambridge 1995

Krantz S.G., Parks H.R.: Geometric Integration Theory. Birkhäuser, Boston 2008

Teaching methods -
Last update: G_M (16.05.2013)


Requirements to the exam - Czech
Last update: prof. RNDr. Jan Rataj, CSc. (12.10.2018)

Zkouška probíhá ústní formou. Její součástí je prezentace vyřešeného předem zadaného cvičení a zodpovězení otázek týkajících se odpřednesené látky.

Syllabus -
Last update: T_MUUK (27.04.2016)

1. k-dimensional Hausdorff measure, Hausdorff dimension, covering theorems, Lebesgue density theorem.

2. Invariant measures on a compact topological group, Haar measure, integral-geometric measure.

3. Disintegration theorem for measures on Cartesian products, existence of regular versions of conditional probabilities, random measure.

Entry requirements -
Last update: prof. RNDr. Jan Rataj, CSc. (15.06.2021)

Basic cousres of mathematical analysis and measure and integration theory.

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