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Positive measure integration

Maruša Turk (2017) Positive measure integration. MSc thesis.

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    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.

    Item Type: Thesis (MSc thesis)
    Keywords: integration, positive measure, Borel sets, σ-algebra, Lebesgue measure, Riesz representation, product measure
    Number of Pages: 49
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Marko SlaparMentor
    asist. dr. Luka Boc ThalerComentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=11870537)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 4919
    Date Deposited: 14 Dec 2017 12:48
    Last Modified: 14 Dec 2017 12:48
    URI: http://pefprints.pef.uni-lj.si/id/eprint/4919

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