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The Decomposition of Measures
Tamara Marković (2019)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Probability and Mathematical Statistics Research Group
Cite this document

Marković, T. (2019). Dekompozicija mjere (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:391869

Marković, Tamara. "Dekompozicija mjere." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:391869

Marković, Tamara. "Dekompozicija mjere." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:391869

Marković, T. (2019). 'Dekompozicija mjere', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 21 November 2019, https://urn.nsk.hr/urn:nbn:hr:126:391869

Marković T. Dekompozicija mjere [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2019 November 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:391869

T. Marković, "Dekompozicija mjere", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:391869

Metadata
TitleDekompozicija mjere
Title (english)The Decomposition of Measures
AuthorTamara Marković
MentorDragana Jankov Maširević (mentor)
Committee memberDragan Jukić (predsjednik povjerenstva)
Committee memberDragana Jankov Maširević (član povjerenstva)
Committee memberIvan Matić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Probability and Mathematical Statistics Research Group)
Osijek
Defense date and country2019-10-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom radu upoznat ćemo se s pojmom mjere s predznakom i njezinim rastavom na razliku dviju mjera. Ovakav rastav omogućuju nam dva teorema koja su u literaturi poznata kao Hahnovova i Jordanova dekompozicija mjere s predznakom. Također, upoznat ćemo se s dekompozicijom σ-konačne mjere na zbroj apsolutno neprekidne i singularne mjere koja je poznata kao Lebesgueova dekompozicija. Rad sadrži puno ilustrativnih primjera koji konkretiziraju ove apstraktne pojmove i tvrdnje.
Abstract (english)
In this paper we will introduce the notion of signed measure and its representation as the difference of two measures. Such representation is enabled by two theorems which are known in the literature as Hahn and Jordan decomposition of signed measure. Also, we will introduce the decomposition of the σ-finite measure into the sum of an absolutely continuous and singular measure, which is known as Lebesgue decomposition. The paper contains many illustrative examples that concretize these abstract concepts and claims.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:391869
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2019-10-14 10:59:20