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Lebesgue measure and Riemann integration

Maruša Turk (2014) Lebesgue measure and Riemann integration. Diploma thesis.

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    Abstract

    In this diploma thesis I introduce the concept of Lebesgue measure on the set of real numbers and show some of the properties of the measure. I will show the existence of Lebesgue non-measurable sets. I will also introduce the concept of a measurable function and give some examples. In the last part of the thesis, I will prove The fundamental theorem of calculus and The Lebesgue characterization for Riemann integrable functions. The latter tells us that a bonded function is Riemann integrabile if and only if it is continuous almost everywhere.

    Item Type: Thesis (Diploma thesis)
    Keywords: Lebesgue measure, outer measure, measurable sets, non-measurable set, measurable functions, Riemann integral, Lebesgue integral
    Number of Pages: 22
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Marko SlaparMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=10174793)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 2361
    Date Deposited: 18 Sep 2014 08:22
    Last Modified: 18 Sep 2014 08:22
    URI: http://pefprints.pef.uni-lj.si/id/eprint/2361

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