A Characterization of Uniform Distribution

Joanna 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 -