Riemann Rearrangement Theorem for some types of convergence

2006/12/28 by Yuriy Dybskiy, Konstantin Slutsky, Dybskiy, Yuriy +1
Computer Science · Mathematics · #40A05 #46B15 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0612840

openalex publication_date 2006/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We reexamine the Riemann Rearrangement Theorem for different types of convergence. We consider series convergence with respect to a filter. We describe the Sum Range (SR) of a series along the 2n-filter and for statistically convergent series.

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