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Measure and Integration Theory II (O) - NMAA170

Title:	Teorie míry a integrálu II (O)
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Is provided by:	NMAA070

Classification:	Mathematics > Real and Complex Analysis
Incompatibility :	NMAA070

Annotation -

Last update: G_M (27.04.2012)

A continuation of the course Measure and Integration Theory I.

Aim of the course -

Last update: G_M (27.04.2012)

Abstract integration and measure theory as a basis for the study of modern mathematical analysis and probability theory. Integral calculus.

Literature - Czech

Last update: G_M (27.04.2012)

W. Rudin: Analýza v reálném a komplexním oboru, Academia, Praha, 2003

J. Lukeš, J. Malý: Míra a integrál (Measure and integral), skripta MFF

J. Kopáček: Matematická analýza pro fyziky III, skripta MFF

J. Lukeš: Příklady z matematické analýzy I. Příklady k teorii Lebesgueova integrálu, skripta MFF

I. Netuka, J. Veselý: Příklady z matematické analýzy. Míra a integrál, skripta MFF

Teaching methods -

Last update: G_M (27.04.2012)

lecture and exercises

Syllabus -

Last update: G_M (27.04.2012)

1. Measure theory.

Construction of Lebesgue measure. Product of measures, abstract Fubini theorem.

2. Integrals depending on a parameter.

Continuity, differentiation. Applications in calculus, Gamma function and Beta function.

3. Integral calculus in R^n.

Fubini's theorem in R^n. Change of variables. Polar, spherical and cylindrical coordinates. Laplace integral.