# A Characterization of Uniform Distribution

Bulletin of the Polish Academy of Sciences. Mathematics (2005)

- Volume: 53, Issue: 2, page 207-220
- ISSN: 0239-7269

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topJoanna Chachulska. "A Characterization of Uniform Distribution." Bulletin of the Polish Academy of Sciences. Mathematics 53.2 (2005): 207-220. <http://eudml.org/doc/280277>.

@article{JoannaChachulska2005,

abstract = {Is the Lebesgue measure on [0,1]² a unique product measure on [0,1]² which is transformed again into a product measure on [0,1]² by the mapping ψ(x,y) = (x,(x+y)mod 1))? Here a somewhat stronger version of this problem in a probabilistic framework is answered. It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y-I(X+Y > 1) and its square given X identifies uniform distribution either absolutely continuous or discrete. No assumptions are imposed on the supports of the distributions of X and Y.},

author = {Joanna Chachulska},

journal = {Bulletin of the Polish Academy of Sciences. Mathematics},

keywords = {constancy of regression; characterization of probability distribution; probability distribution on algebraic structures},

language = {eng},

number = {2},

pages = {207-220},

title = {A Characterization of Uniform Distribution},

url = {http://eudml.org/doc/280277},

volume = {53},

year = {2005},

}

TY - JOUR

AU - Joanna Chachulska

TI - A Characterization of Uniform Distribution

JO - Bulletin of the Polish Academy of Sciences. Mathematics

PY - 2005

VL - 53

IS - 2

SP - 207

EP - 220

AB - Is the Lebesgue measure on [0,1]² a unique product measure on [0,1]² which is transformed again into a product measure on [0,1]² by the mapping ψ(x,y) = (x,(x+y)mod 1))? Here a somewhat stronger version of this problem in a probabilistic framework is answered. It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y-I(X+Y > 1) and its square given X identifies uniform distribution either absolutely continuous or discrete. No assumptions are imposed on the supports of the distributions of X and Y.

LA - eng

KW - constancy of regression; characterization of probability distribution; probability distribution on algebraic structures

UR - http://eudml.org/doc/280277

ER -

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