Abstract: On arbitrary topological groups a natural finitely additive measure can be defined via compactifications. It is closely related to Hartman's concept of uniform distribution on non-compact groups (cf. S. Hartman, Remarks on equidistribution on non-compact groups, Comp. Math. 16 (1964) 66-71). Applications to several situations are possible.

Some results of M. Pasteka and other authors on uniform distribution with respect to translation invariant finitely additive probability measures on Dedekind domains are transfered to more general situations. Furthermore it is shown that the range of a polynomial of degree >1 on a ring of algebraic integers has measure 0.

PDF: Frisch, Pasteka, Tichy, Winkler: Finitely additive measures on groups and rings

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