On the Skitovich-Darmois Theorem on Abelian Groups

• Date: 2004
• Main Authors: Myronyuk, M. V., Миронюк, М. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3847
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove theorems that generalize the Skitovich-Darmois theorem to the case where independent random variables ξj, j = 1, 2, ..., n, n ≥ 2, take values in a locally compact Abelian group and the coefficients αj and βj of the linear forms L 1 = α1ξ1 + ... + αnξn and L 2 = β1ξ1 + ... + βnξn are automo...