Levy-Steinitz for countable sets of series

TL;DR

This paper extends the Levy-Steinitz theorem to sequences of countable sequences of real numbers, providing a broader understanding of the possible limits under permutations in the context of pointwise convergence.

Contribution

It generalizes the Levy-Steinitz theorem to countable sequences of sequences, reestablishing a result originally proved by Troyanski.

Findings

Extended Levy-Steinitz characterization to countable sequences

Reproved a theorem of Troyanski in this new context

Broadened understanding of permutation limits in series

Abstract

The Levy-Steinitz theorem characterizes the values that a conditionally convergent sequence in of real numbers can attain under permutations. We extend this analysis to sequences of countable sequences of real numbers, under pointwise convergence, reproving a theorem of Stanimir Troyanski.