The Riemann theorem and divergent permutations

Wituła, Roman

Colloquium Mathematicae, Tome 70 (1996), p. 275-287 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper the fundamental algebraic propeties of convergent and divergent permutations of ℕ are presented. A permutation p of ℕ is said to be divergent if at least one conditionally convergent series $∑ a_n$ of real terms is rearranged by p to a divergent series $∑ a_{p(n)}$. All other permutations of ℕ are called convergent. Some generalizations of the Riemann theorem about the set of limit points of the partial sums of rearrangements of a given conditionally convergent series are also studied.

Détail

Publié le : 1996-01-01

Zbl 0840.40002

EUDML-ID : urn:eudml:doc:210341

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