Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

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 to 2023
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
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

Opinion survey results Examination dates Schedule Noticeboard

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)

Lecture.

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.