On Riemann's Theorem About Conditionally Convergent Series

TL;DR

This paper generalizes Riemann's theorem on rearranging conditionally convergent series from single sums to multiple sums, expanding the understanding of series rearrangements in higher dimensions.

Contribution

It introduces a novel extension of Riemann's theorem to multiple sums, providing new insights into the behavior of conditionally convergent series in multiple dimensions.

Findings

Extended Riemann's theorem to multiple sums

Demonstrated flexibility in rearranging conditionally convergent series in higher dimensions

Provided theoretical framework for multiple sum rearrangements

Abstract

We extend Riemann's rearrangement theorem on conditionally convergent series of real numbers to multiple instead of simple sums.