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Kolmogorov-Smirnov isometries of the space of generalized distribution functions

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Mathematica Slovaca

Abstract

In this paper we describe the structure of surjective isometries of the space of all generalized probability distribution functions on ℝ with respect to the Kolmogorov-Smirnov metric.

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References

  1. DOLINAR, G.— MOLNÁR, L.: Isometries of the space of distribution functions with respect to the Kolmogorov-Smirnov metric, J. Math. Anal. Appl. 348 (2008), 494–498.

    Article  MATH  MathSciNet  Google Scholar 

  2. FELLER, W.: An Introduction to Probability Theory and its Applications, Vol. II, John Wiley and Sons, New York, 1971.

    MATH  Google Scholar 

  3. FLEMING, R. J.— JAMISON, J. E.: Isometries on Banach Spaces: Function Spaces. Vol. 1. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 129, CRC Press, Boca Raton, FL, 2002.

    Google Scholar 

  4. FLEMING, R. J.— JAMISON, J. E.: Isometries on Banach Spaces: Vector-valued Function Spaces. Vol. 2. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. 138, CRC Press, Boca Raton, FL, 2007.

    Book  Google Scholar 

  5. MOLNÁR, L.: Kolmogorov-Smirnov isometries and affine automorphisms of spaces of distribution functions, Cent. Eur. J. Math. 9 (2011), 789–796.

    Article  MATH  MathSciNet  Google Scholar 

  6. SHIRYAEV, A. N.: Probability. Grad. Texts in Math. 95, Springer-Verlag, Berlin, 1996.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, H-4010, Debrecen, P.O. Box 12, Hungary

    Lajos Molnár & Patrícia Szokol

Authors
  1. Lajos Molnár
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  2. Patrícia Szokol
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Corresponding author

Correspondence to Lajos Molnár.

Additional information

Communicated by Werner Timmermann

The first author was supported by the Hungarian Scientific Research Fund (OTKA), Grant No. K81166 NK81402, and also by the TÁMOP 4.2.1./B-09/1/KONV-2010-0007 project implemented through the New Hungary Development Plan co-financed by the European Social Fund and the European Regional Development Fund. The second author was supported by the TÁMOP-4.2.2/B-10/1-2010-0024 project co-financed by the European Union and the European Social Fund.

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Molnár, L., Szokol, P. Kolmogorov-Smirnov isometries of the space of generalized distribution functions. Math. Slovaca 64, 433–444 (2014). https://doi.org/10.2478/s12175-014-0216-8

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  • DOI: https://doi.org/10.2478/s12175-014-0216-8

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