International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 1, Pages 1-37

Moments of probability measures on a group

Herbert Heyer

Mathematisches Institut der Universität, Auf der Morgenstelle 10, Tübingen D-7400, Germany

Received 28 October 1980

Copyright © 1981 Herbert Heyer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


New developments and results in the theory of expectatiors and variances for random variables with range in a topological group are presented in the following order (i) Introduction (2) Basic notions (3) The three series theorem in Banach spaces (4) Moment Conditions (5) Expectations and variances (6) A general three series theorem (7) The special cases of finite groups and Lie groups (8)The strong laws of large numbers on a Lie group (9) Further studies on moments of probability measures.