Integracija in pozitivna mera
Turk, Maruša (Author), Slapar, Marko (Mentor) More about this mentor... , Boc Thaler, Luka (Co-mentor)

 URL - Presentation file, Visit http://pefprints.pef.uni-lj.si/4919/

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 integracija Master's thesis/paper (mb22) 2.09 - Master's Thesis PEF - Faculty of Education 2017 11870537 275 87 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

## Secondary language

Language: English Positive measure integration 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. integration