Finitely additive measures on groups and rings
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On 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. ). Applications to several situations are possible. Some results of M. Paštéka and other authors on uniform distribution with respect to translation invariant finitely additive probability measures on Dedekind domains are transferred to more general situations. Furthermore it is shown that the range of a polynomial of degree ≥2 on a ring of algebraic integers has measure 0.
KeywordsHaar Measure Finite Index Ideal Measure Algebraic Integer Dedekind Domain
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- Paštéka M.,The measure density on Dedekind domains, Ricerche di matematica,45, to appear.Google Scholar
- Paštéka M.,Submeasures and uniform distribution on Dedekind rings, Tatra Mountain Math. Publ., to appear.Google Scholar
- Paštéka M., Tichy R. F.,Distribution problems in Dedekind domains and submeasures, Ann. Univ. Ferrara,40 (1994), 191–206.Google Scholar
- van der Waerden B. L.,Algebra I+II, Springer, Berlin, 1967.Google Scholar
- Wan D.,A p-adic Lifting Lemma and Its Applications to Permutation Polynomials, in “Finite Fields, Coding Theory, and Advances in Computing” (Proc. of Conf. in Las Vegas, Nevada, 1991), G. L. Mullen and P. J.-S. Shiue eds., Dekker, 1993.Google Scholar