Convergence of measurable functions in the sense of density

Altinok, MayaKucukaslan, MehmetUnay, A. Kerem2025-03-172025-03-1720230971-36112367-2501https://doi.org/10.1007/s41478-022-00529-4https://hdl.handle.net/20.500.13099/2269In this paper, by using unbounded modulus function the notion mu(f)-density for measurable subsets of I = [1, infinity] is defined and related notion mu f-statistical convergence of measurable functions is investigated. In addition to the basic properties of mu(f)-density and mu(f)-statistical convergence, the definition of being mu(f)-Cauchy is given and it is shown that these two concepts are equivalent for real valued measurable functions. Among others, the notion of f-strongly Cesaro summability is introduced. Finally, necessary and sufficient conditions between f-strongly Cesaro summability and mu(f)-statistical convergence are given under explicated restrictions on measurable function and modulus function.eninfo:eu-repo/semantics/closedAccessConvergenceStatistical convergenceMeasurable functionsModulus functionConvergence of measurable functions in the sense of densityArticle10.1007/s41478-022-00529-431214871510N/AWOS:000896445900001Q2