Abstract
This is a continuation of the paper [6]. The concept of discrepancy of a sequence in a compact abelian group with second countability axiom is now investigated in its relation to problems of distribution and approximation. Some fundamental inequalities of the theory of uniform distribution mod 1 can be transferred to the general case, e.g. Koksma's inequality. The crucial point in the generalization of Koksma's inequality is the suitable definition of total variation. Another version of this inequality with an upper bound in terms of the Fourier coefficients is presented. Aardenne-Ehrenfest's theorem is valid for non totally disconnected groups.
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