Daylen K. Thimm, On a meager full measure subset of N-ary sequences

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DOI: 10.23952/asvao.6.2024.1.07
Volume 6, Issue 1, 1 April 2024, Pages 81-86

Abstract. Let $I=\{1,\dots,N\}$ be a finite set of indices and $K=I^{\mathbb{N}}$ the set of all sequences of indices equipped with the product measure and the product topology. Melo, da Cruz Neto, and de Brito [Strong convergence of alternating projections, J. Optim. Theory Appl. 194 (2022), 306-324] defined a family of sequences $\mathcal{N}_0\subseteq K$ so that whenever one iterates distance minimizing projections on $N$ closed and convex subsets of an Hadamard space, the sequence of projections converges, provided it has at least one accumulation point. They proved that $\mathcal{N}_0$ has full measure, and in the sense of measure almost all iterates of projections converge. We observe that $\mathcal{N}_0$ is meager. The question, which almost all iterates converge in the topological sense, remains open.

How to Cite this Article:
D.K. Thimm, On a meager full measure subset of N-ary sequences, Appl. Set-Valued Anal. Optim. 6 (2024), 81-86.