It is the aim of this paper to generalize the notion of discrepancy of a sequence to compact abelian groups satisfying the second axiom of countability. This concept of discrepancy which depends heavily on the study of certain generating subsets of the character group includes the hitherto known case of the n-dimensional unit cube. The definition is subsequently justified by transferring well-known theorems of the classical theory to the general case. This first part mainly deals with the algebraic point of view which doesn't possess an analogy in the theory of uniform distribution mod 1. The proofs involve a lot of group theoretic argument. Theorems concerning distribution and approximation will be presented in the second part.
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