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Matematicheskie Zametki, 1996, Volume 59, Issue 2, Pages 267–277
DOI: https://doi.org/10.4213/mzm1713 (Mi mzm1713) 		 
This article is cited in 3 scientific papers (total in 3 papers)

On the Marcinkiewicz theorem for the binary Perron integral

V. A. Skvortsov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (182 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm1713
Abstract: A criterion for Perron integrability of the derivative of a function is stated in terms of the variation of the function with respect to a differential base. The criterion is used to construct an example showing that the Marcinkiewicz theorem, which asserts that ordinary Perron integrability follows from the existence of at least one continuous Perron minorant and at least one continuous Perron majorant, cannot be generalized to the binary Perron integral.
Received: 21.04.1995
English version:
Mathematical Notes, 1996, Volume 59, Issue 2, Pages 189–195
DOI: https://doi.org/10.1007/BF02310959
Bibliographic databases:
UDC: 517.98
Language: Russian
Citation: V. A. Skvortsov, “On the Marcinkiewicz theorem for the binary Perron integral”, Mat. Zametki, 59:2 (1996), 267–277; Math. Notes, 59:2 (1996), 189–195
Citation in format AMSBIB
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\paper On~the Marcinkiewicz theorem for the binary Perron integral
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\pages 189--195
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  • https://doi.org/10.4213/mzm1713
  • https://www.mathnet.ru/eng/mzm/v59/i2/p267
    • This publication is cited in the following 3 articles:
    1. Tulone F. Skvortsov V., “Multidimensional P-Adic Integrals in Some Problems of Harmonic Analysis”, Minimax Theory Appl., 2:1, SI (2017), 153–174  mathscinet  zmath  isi
    2. V. A. Sklyarenko, “On a property of the Burkill SCP-integral”, Math. Notes, 65:4 (1999), 500–505  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. A. Skvortsov, “Variations and variational measures in integration theory and some applications”, J Math Sci, 91:5 (1998), 3293  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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