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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