Integracija in pozitivna mera

magistrsko delo

Maruša Turk (Author), Marko Slapar (Mentor), Luka Boc Thaler (Co-mentor)

Abstract

V diplomskem delu smo se osredotočili na vpeljavo Lebesguove mere na množico realnih števil in vpeljali Lebesguov integral, ki odpravi določene teoretične pomanjkljivosti Riemannovega integrala. Lebesguov integral nam med drugim omogoči precej boljše razumevanje osnovnega izreka integralskega računa. V magistrskem delu bomo obravnavali splošno teorijo integracije pozitivne mere na nekem merljivem prostoru. Videli bomo, da lahko teorijo številskih vrst med drugim razumemo kot teorijo integracije funkcij, definiranih na naravnih številih z običajno diskretno mero. Prav tako bomo s pomočjo Rieszovega izreka na nov način vpeljali Lebesgueovo mero. V zadnjem poglavju bomo vpeljali produktno mero.

Keywords

Borelove množice;algebra;Lebesguova mera;Rieszov reprezentacijski izrek;produktna mera;

Data

Language:	Slovenian
Year of publishing:	2017
Typology:	2.09 - Master's Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[M. Turk]
UDC:	51(043.2)
COBISS:	11870537
Views:	779
Downloads:	168
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Positive measure integration
Secondary abstract:	In the diploma thesis we focused on the introduction of Lebesgue measure on a set of real numbers and introduced the Lebesgue integral, which removes certain theoretical weaknesses of the Riemann integral. Lebesgue integrals also provied us with a better understanding of the fundamental theorem of calculus. In the master's thesis we will deal with the general theory of integration of a positive measure in a measurable space. Among other things, we will be able to consider sums of number series as a theory of integration of functions defined on natural numbers with the usual counting measure. We will also use the Riesz representation theorem to give an alternative description of the Lebesgue measure. In the last chapter, product measures will be introduced.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Poučevanje, Predmetno poučevanje, Matematika in fizika
Pages:	49 f.
ID:	10889363