Levy-Steinitz for countable sets of series

2018/02/10 by Larson, Paul B.
#40A30 #40B05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.03509

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.

Related

• Levy-Steinitz theorem and achievement sets of conditionally convergent series on the real plane
• A simple inductive proof of Levy-Steinitz theorem
• A Colorful Steinitz Lemma with Applications to Block Integer Programs
• Convergence of sequences: a survey
• A generalization of Piatetski-Shapiro sequences (II)