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Ukrainian Mathematical Journal

, Volume 70, Issue 8, pp 1264–1274 | Cite as

Upper and Lower Lebesgue Classes of Multivalued Functions of Two Variables

  • O. Karlova
  • V. Mykhailyuk
Article

We introduce a functional Lebesgue classification of multivalued mappings and obtain results on the upper and lower Lebesgue classifications of multivalued mappings F: X × YZ for broad classes of spaces X, Y and Z.

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References

  1. 1.
    T. Banakh, “(Metrically) quarter-stratifiable spaces and their applications,” Mat. Stud., 18, No. 1, 10–28 (2002).MathSciNetzbMATHGoogle Scholar
  2. 2.
    M. Burke, “Borel measurability of separately continuous functions,” Topol. Appl., 129, No. 1, 29–65 (2003).MathSciNetCrossRefGoogle Scholar
  3. 3.
    R. Engelking, General Topology, Heldermann, Berlin (1989).zbMATHGoogle Scholar
  4. 4.
    O. Karlova, “Baire classification of maps which are continuous with respect to the first variable and of the functional Lebesgue class α with respect to the second one,” Math. Bull. Shevchenko Sci. Soc., 2, 98–114 (2004).Google Scholar
  5. 5.
    O. Karlova and O. Sobchuk, “Lebesgue classification of multivalued maps of two variables,” Nauk. Visn. Cherniv. Univ. Mat., 160, 76–79 (2003).zbMATHGoogle Scholar
  6. 6.
    K. Kuratowski, “Sur la théorie des fonctions dans les espaces métriques,” Fund. Mat., 17, 275–282 (1931).CrossRefGoogle Scholar
  7. 7.
    K. Kuratowski, “Quelques problèmes concernant les espaces métriques non-séparables,” Fund. Mat., 25, 533–545 (1935).zbMATHGoogle Scholar
  8. 8.
    G. Kwiecińska, “On Lebesgue theorem for multivalued functions of two variables,” in: Proc. of the Ninth Prague Topological Symp. (Prague, August 19–25, 2001), pp. 181–189.Google Scholar
  9. 9.
    H. Lebesgue, “Sur les fonctions représentables analytiquement,” J. Math. Pures Appl., 1, No. 6, 139–216 (1905).zbMATHGoogle Scholar
  10. 10.
    O. Maslyuchenko, V. Maslyuchenko, and V. Mykhaylyuk, “Paracompactness and Lebesgue’s classifications,” Mat. Met. Fiz.-Mekh. Polya, 47, No. 2, 65–72 (2004).MathSciNetGoogle Scholar
  11. 11.
    O. Maslyuchenko, V. Maslyuchenko, V. Mykhaylyuk, and O. Sobchuk, “Paracompactness and separately continuous mappings,” in: General Topology in Banach Spaces, Nova Science, New York (2001), pp. 147–169.Google Scholar
  12. 12.
    D. Montgomery, “Non separable metric spaces,” Fund. Mat., 25, 527–533 (1935).CrossRefGoogle Scholar
  13. 13.
    V. V. Mykhaylyuk, “Baire classification of separately continuous functions and Namioka property,” Ukr. Mat. Bul., 5, No. 2, 203–218 (2008).MathSciNetGoogle Scholar
  14. 14.
    O. V. Sobchuk, “PP-spaces and Baire classifications,” in: Proc. of the Int. Conf. on Functional Analysis and Its Applications Dedicated to the 110th Birthday of Stefan Banach (Lviv, May 28–31, 2002), p. 189.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • O. Karlova
    • 1
  • V. Mykhailyuk
    • 1
    • 2
  1. 1.Fed’kovych Chernivtsi National UniversityChernivtsiUkraine
  2. 2.J. Kochanowski University in KielceKielcePoland

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