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.


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


Borel classes
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