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Izv. Akad. Nauk SSSR Ser. Mat., 1972, Volume 36, Issue 2, Pages 435–449 (Mi izv2304)  

This article is cited in 5 scientific papers (total in 5 papers)

Adjoint functions and integrals

T. P. Lukashenko


Abstract: In this paper it is proved that $A$-integrals and $B$-integrals are inconsistent with the Denjoy–Hincin integral of functions which are adjoint to a summable function. Furthermore, the paper establishes nonadditivity of the $B$-integrals on an interval.

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English version:
Mathematics of the USSR-Izvestiya, 1972, 6:2, 429–443

Bibliographic databases:

UDC: 517.5
MSC: Primary 28A30; Secondary 42A40
Received: 22.06.1971

Citation: T. P. Lukashenko, “Adjoint functions and integrals”, Izv. Akad. Nauk SSSR Ser. Mat., 36:2 (1972), 435–449; Math. USSR-Izv., 6:2 (1972), 429–443

Citation in format AMSBIB
\Bibitem{Luk72}
\by T.~P.~Lukashenko
\paper Adjoint functions and integrals
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1972
\vol 36
\issue 2
\pages 435--449
\mathnet{http://mi.mathnet.ru/izv2304}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=306416}
\zmath{https://zbmath.org/?q=an:0244.42023}
\transl
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 2
\pages 429--443
\crossref{https://doi.org/10.1070/IM1972v006n02ABEH001881}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. T. P. Lukashenko, “On $D$-integrable conjugate functions”, Math. USSR-Izv., 7:4 (1973), 949–962  mathnet  crossref  mathscinet  zmath
    2. T. P. Lukashenko, “Denjoy–Khinchin-integrable functions and their conjugates”, Math. USSR-Izv., 11:3 (1977), 625–664  mathnet  crossref  mathscinet  zmath
    3. T. P. Lukashenko, “Conjugate functions and the restricted Denjoy integral”, Math. USSR-Sb., 33:1 (1977), 81–124  mathnet  crossref  mathscinet  zmath  isi
    4. T. P. Lukashenko, “On integrals of conjugate functions”, Math. USSR-Izv., 15:1 (1980), 53–86  mathnet  crossref  mathscinet  zmath  isi
    5. T. P. Lukashenko, “On functions of generalized bounded variation”, Math. USSR-Izv., 20:2 (1983), 267–301  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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