# Kolmogorov-Smirnov isometries and affine automorphisms of spaces of distribution functions

Open Mathematics (2011)

- Volume: 9, Issue: 4, page 789-796
- ISSN: 2391-5455

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topLajos Molnár. "Kolmogorov-Smirnov isometries and affine automorphisms of spaces of distribution functions." Open Mathematics 9.4 (2011): 789-796. <http://eudml.org/doc/269464>.

@article{LajosMolnár2011,

abstract = {In this paper we describe the structure of surjective isometries of the spaces of all absolutely continuous, singular, or discrete probability distribution functions on R equipped with the Kolmogorov-Smirnov metric. We also study the structure of affine automorphisms of the space of all distribution functions.},

author = {Lajos Molnár},

journal = {Open Mathematics},

keywords = {Kolmogorov-Smirnov metric; Absolute continuous distribution functions; Singular distribution functions; Discrete distribution functions; Isometry; absolute continuous distribution functions; singular distribution functions; discrete distribution functions; isometry},

language = {eng},

number = {4},

pages = {789-796},

title = {Kolmogorov-Smirnov isometries and affine automorphisms of spaces of distribution functions},

url = {http://eudml.org/doc/269464},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Lajos Molnár

TI - Kolmogorov-Smirnov isometries and affine automorphisms of spaces of distribution functions

JO - Open Mathematics

PY - 2011

VL - 9

IS - 4

SP - 789

EP - 796

AB - In this paper we describe the structure of surjective isometries of the spaces of all absolutely continuous, singular, or discrete probability distribution functions on R equipped with the Kolmogorov-Smirnov metric. We also study the structure of affine automorphisms of the space of all distribution functions.

LA - eng

KW - Kolmogorov-Smirnov metric; Absolute continuous distribution functions; Singular distribution functions; Discrete distribution functions; Isometry; absolute continuous distribution functions; singular distribution functions; discrete distribution functions; isometry

UR - http://eudml.org/doc/269464

ER -

## References

top- [1] Dolinar G., Molnár L., Isometries of the space of distribution functions with respect to the Kolmogorov-Smirnovmetric, J. Math. Anal. Appl.,2008, 348(1), 494–498 http://dx.doi.org/10.1016/j.jmaa.2008.07.054 Zbl1162.46305
- [2] Yeh J., Real Analysis: Theory of Measure and Integration, 2nd ed., World Scientific, Hackensack, 2006 Zbl1098.28002

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