TY - JOUR
AU - P. Graczyk
AU - G. M. Fel'dman
PY - 2001/04/25
Y2 - 2024/11/02
TI - Independent Linear Statistics on Finite Abelian Groups
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 53
IS - 4
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/4266
AB - We give a complete description of the class of all finite Abelian groups X for which the independence of linear statistics L 1 = α1(ξ1) + α2(ξ2) + α3(ξ3) and L 2 = β1(ξ1) + β2(ξ2) + β3(ξ3) (here, ξ j , j = 1, 2, 3, are independent random variables with values in X and distributions μ j ; α j and β j are automorphisms of X) implies that either one, or two, or three of the distributions μ j are idempotents.
ER -