Skitovich–Darmois Theorem for Discrete and Compact Totally Disconnected Abelian Groups

• Date: 2013
• Main Authors: Mazur, I. P., Мазур, И. П.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2480
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The classic Skitovich–Darmois theorem states that the Gaussian distribution on the real line can be characterized by the independence of two linear forms of n independent random variables. We generalize the Skitovich–Darmois theorem to discrete Abelian groups, compact totally disconnected Abelian gr...