We study and solve several functional equations which yield necessary and sufficient conditions for the sum of two uniformly distributed random variables to be uniformly distributed.
@article{urn:eudml:doc:38815, title = {On sums of dependent uniformly distributed random variables.}, journal = {Stochastica}, volume = {3}, year = {1979}, pages = {33-43}, zbl = {0418.39007}, mrnumber = {MR0556646}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38815} }
Alsina, Claudi; Bonet, Eduard. On sums of dependent uniformly distributed random variables.. Stochastica, Tome 3 (1979) pp. 33-43. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38815/