# The Riemann theorem and divergent permutations

Colloquium Mathematicae (1996)

- Volume: 69, Issue: 2, page 275-287
- ISSN: 0010-1354

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topWituła, Roman. "The Riemann theorem and divergent permutations." Colloquium Mathematicae 69.2 (1996): 275-287. <http://eudml.org/doc/210341>.

@article{Wituła1996,

abstract = {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.},

author = {Wituła, Roman},

journal = {Colloquium Mathematicae},

keywords = {permutations; series; Riemann theorem; limit points; partial sums; rearrangements},

language = {eng},

number = {2},

pages = {275-287},

title = {The Riemann theorem and divergent permutations},

url = {http://eudml.org/doc/210341},

volume = {69},

year = {1996},

}

TY - JOUR

AU - Wituła, Roman

TI - The Riemann theorem and divergent permutations

JO - Colloquium Mathematicae

PY - 1996

VL - 69

IS - 2

SP - 275

EP - 287

AB - 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.

LA - eng

KW - permutations; series; Riemann theorem; limit points; partial sums; rearrangements

UR - http://eudml.org/doc/210341

ER -

## References

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- [21] R. Wituła, On the set of limit points of the partial sums of series rearranged by a given divergent permutation, J. Math. Anal. Appl., to appear. Zbl1187.40007
- [22] R. Wituła, Convergent and divergent permutations--the algebraic and analytic properties, in preparation. Zbl1313.40004
- [23] R. Wituła, Convergence-preserving functions, Nieuw Arch. Wisk., to appear. Zbl0858.40004

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