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Integracija in pozitivna mera
Turk, Maruša (Author), Slapar, Marko (Mentor) More about this mentor... This link opens in a new window, Boc Thaler, Luka (Co-mentor)

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/4919/ This link opens in a new window

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.

Language:Slovenian
Keywords:integracija
Work type:Master's thesis/paper (mb22)
Tipology:2.09 - Master's Thesis
Organization:PEF - Faculty of Education
Year:2017
COBISS.SI-ID:11870537 Link is opened in a new window
Views:275
Downloads:87
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Secondary language

Language:English
Title:Positive measure integration
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.

Keywords:integration

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