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On Nonmeasurable Functions of Two Variables and Iterated Integrals

On Nonmeasurable Functions of Two Variables and Iterated Integrals Following the paper of Pkhakadze Trudy Tbiliss. Mat. Inst. Razmadze 20: 167–209, 1954, we consider some properties of real-valued functions of two variables, which are not assumed to be measurable with respect to the two-dimensional Lebesgue measure on the plane 𝐑 2 , but for which the corresponding iterated integrals exist and are equal to each other. Close connections of these properties with certain set-theoretical axioms are emphasized. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

On Nonmeasurable Functions of Two Variables and Iterated Integrals

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References (12)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2009.705
Publisher site
See Article on Publisher Site

Abstract

Following the paper of Pkhakadze Trudy Tbiliss. Mat. Inst. Razmadze 20: 167–209, 1954, we consider some properties of real-valued functions of two variables, which are not assumed to be measurable with respect to the two-dimensional Lebesgue measure on the plane 𝐑 2 , but for which the corresponding iterated integrals exist and are equal to each other. Close connections of these properties with certain set-theoretical axioms are emphasized.

Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2009

Keywords: Nonmeasurable function; iterated integral; continuum hypothesis; Sierpiński's decomposition of the square

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