Published online by Cambridge University Press: 24 October 2008
1Introduction. In this paper, I give a definition of uniform distribution for sequences taking values in certain types of Abelian group—in particular, in groups of prime exponent—and one of independent distribution for sets of such sequences. In the various cases, I find conditions for the properties to hold, which are similar to Weyl's criterion for the uniform distribution of real sequences modulo 1.