We consider the generalized Egorov’s statement (Egorov’s Theorem without the assumption on measurability of the functions, see Weiss (2004)) in the case of an ideal convergence and a number of different types of ideal convergence notions. We prove that in those cases the generalized Egorov’s statement is independent from ZFC.
"A Generalized Egorov’s Statement for Ideals." Real Anal. Exchange 42 (2) 269 - 282, 2017. https://doi.org/10.14321/realanalexch.42.2.0269