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Baire’s space of permutations of \(N\) and rearrangements of series. (English) Zbl 1007.54032

The classical theorem of Riemann says that a non-absolutely converging series \(\sum_{k=1}^\infty a_k\), with real terms, can be rearranged with the help of a permutation \(\sigma:N\to N\), so that the associated sum \(\sum_{i=1}^\infty a_{\sigma(i)}\) has any value prescribed in advance. The author studies the metric space of all rearrangements of a series of this type as well as some of its distinguished subclasses from the point of view of descriptive set theory.

MSC:

54E52 Baire category, Baire spaces
26A21 Classification of real functions; Baire classification of sets and functions
40A05 Convergence and divergence of series and sequences

Keywords:

Borel classes
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