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master's thesis
Teorija mjere
2019. urn:nbn:hr:166:841975
Krišto, Arbi
University of Split
University of Split, Faculty of science
Department of Mathematics

Cite this document

Krišto, A. (2019). Teorija mjere (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:841975

Krišto, Arbi. "Teorija mjere." Master's thesis, University of Split, University of Split, Faculty of science, 2019. https://urn.nsk.hr/urn:nbn:hr:166:841975

Krišto, Arbi. "Teorija mjere." Master's thesis, University of Split, University of Split, Faculty of science, 2019. https://urn.nsk.hr/urn:nbn:hr:166:841975

Krišto, A. (2019). 'Teorija mjere', Master's thesis, University of Split, University of Split, Faculty of science, accessed 26 May 2022, https://urn.nsk.hr/urn:nbn:hr:166:841975

Krišto A. Teorija mjere [Master's thesis]. Split: University of Split, University of Split, Faculty of science; 2019 [cited 2022 May 26] Available at: https://urn.nsk.hr/urn:nbn:hr:166:841975

A. Krišto, "Teorija mjere", Master's thesis, University of Split, University of Split, Faculty of science, Split, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:166:841975

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Metadata
TitleTeorija mjere
Title (english)Measure theory
AuthorArbi Krišto
MentorSnježana Braić (mentor)
Committee memberSnježana Braić (predsjednik povjerenstva)
Committee memberGoran Erceg (član povjerenstva)
Committee memberIvan Jelić (član povjerenstva)
GranterUniversity of Split
University of Split, Faculty of science
(Department of Mathematics)
Split
Defense date and country2019-11-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Cilj ovoga rada je obraditi temeljne pojmove koji se vežu uz teoriju mjere. U tu svrhu smo definirali opu mjeru i osnovna svojstva mjere. Time smo bili u mogunosti da definiramo vanjsku i Lebesgueovu mjeru koje su nam kasnije koristile za obraditi izmjerive funkcije i svojstva povezana s njima. Na kraju drugog poglavlja definirali smo jednostavne funkcije koje su jako važne za integrabilne funkcije. Da bismo definirali integrabilne funkcije prvo smo definirali integrale nenegativnih funkcija i integrale izmjerivih funkcija, pa nakon toga integrabilne funkcije. Tada smo također iskazali i dokazali neke važne teoreme kao što su ”Levijev teorem o monotonoj konvergenciji” ili ”Lebesgueov teorem o dominiranoj konvergenciji”. Ovaj diplomski rad završili smo povezivanjem Riemannovog i Lebesgu eovog integrala jer je Lebesgueov integral definiran za puno širu klasu funkcija od klase omeđenih funkcija.
Abstract (english)
The aim of this paper is to address the basic concepts that bind to measure theory. For this purpose, we have defined the general measure and the basic properties of the measure. In doing so, we were able to define the external and Lebesgue measures that were later used to explain measurable functions and properties associated with them. At the end of Chapter two, we have defined simple functions that are very important for integrable functions. To define integrable functions, we first define integrals of nonnegative functions and integrals of measurable func tions, and then integrable functions. After that we also proved and proved some important theorems such as ”Levi’s Monotone Convergence Theorem” or ”Lebesgue Domination Convergence Theorem”. We ended this thesis by connecting Riemann’s and Lebesgue’s integrals because the Lebesgue integral is defined for a much wider class of functions than the class of bounded functions.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:841975
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching
Course: major in pure mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to authenticated users
Terms of useLicence In copyright icon
Created on2019-12-18 14:47:17