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Journal of Soviet Mathematics

, Volume 31, Issue 1, pp 2721–2729 | Cite as

Functions of the first Baire class with values in metric spaces and some applications of them

  • O. I. Reinov
Article

Abstract

The classical Baire characterization of functions of the first Baire class in terms of points of continuity is carried over to functions with values in certain metric spaces. As corollaries we get new characterizations of Radon-Nikodym operators.

Keywords

Baire Class 
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Literature cited

  1. 1.
    H. P. Rosenthal, “Pointwise compact subsets of the first Baire class,” Am. J. Math.,99, No. 2, 362–378 (1977).Google Scholar
  2. 2.
    E. Odell and H. P. Rosenthal, “A double-dual characterization of separable Banach spaces containingl 1,” Israel J. Math.,20, Nos. 3–4, 375–384 (1975).Google Scholar
  3. 3.
    A. Grothendieck, “Produits tensoriels topologiques et espaces nucleaires,” Mem. Am. Math. Soc., 16 (1955).Google Scholar
  4. 4.
    I. P. Natanson, Theory of Functions of a Real Variable [in Russian], Nauka, Moscow (1974).Google Scholar
  5. 5.
    P. S. Aleksandrov and P. S. Uryson, Memoir on Compact Topological Spaces [in Russian], Nauka, Moscow (1971).Google Scholar
  6. 6.
    C. Stegall, “The Radon-Nikodym property in conjugate Banach spaces,” Trans. Am. Math. Soc.,206, 213–223 (1975).Google Scholar
  7. 7.
    N. Bourbaki, General Topology [Russian translation], Vol. 3, Nauka (1975).Google Scholar
  8. 8.
    R. Haydon, “Some more characterizations of Banach spaces containing 1,” Math. Proc. Cambridge Philos. Soc.,80, No. 2, 269–276 (1976).Google Scholar
  9. 9.
    W. J. Davis, T. Figiel, W. B. Johnson, and A. Pelczynski, “Factoring weakly compact operators,” J. Funct. Anal.,17, No. 3, 311–327 (1974).CrossRefGoogle Scholar
  10. 10.
    O. I. Reinov, “Operators of type RN in Banach spaces,” Dokl. Akad. Nauk SSSR,220, No. 3, 528–531 (1975).Google Scholar
  11. 11.
    O. I. Reinov, “Two questions in the theory of linear operators,” in: Applications of Functional Analysis to the Theory of Approximations (Kalinin) [in Russian], Vol. 9 (1979).Google Scholar
  12. 12.
    O. I. Reinov, “RN-sets in Banach spaces,” Funkts. Analiz Prilozhen.,12, No. 1, 80–81 (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • O. I. Reinov

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