ON A MEAGER FULL MEASURE SUBSET OF N-ARY SEQUENCES.

Let I = {1;: :: ;N} be a finite set of indices and K = IN 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 N₀ ⊆ 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 N₀ has full measure, and in the sense of measure almost all iterates of projections converge. We observe that N₀ is meager. The question, which almost all iterates converge in the topological sense, remains open. [ABSTRACT FROM AUTHOR]