Abstract
By using unbounded modulus functions we introduce a new concept of density for sets of pairs of natural numbers. Consequently, we obtain a generalization of the notion of statistical convergence of double sequences which is studied and characterized. As an application, we prove that `Pringsheim convergence' is equivalent to `module statistical convergence for every unbounded modulus function'.
Citation
A. Aizpuru. M. Listán-García. F. Rambla-Barreno. "Double density by moduli and statistical convergence." Bull. Belg. Math. Soc. Simon Stevin 19 (4) 663 - 673, november 2012. https://doi.org/10.36045/bbms/1353695907
Information