Generalized Egorov's statement for ideals

TL;DR

This paper investigates the generalized Egorov's statement in the context of ideal convergence, demonstrating its independence from ZFC across various types of ideal convergence notions.

Contribution

It extends Egorov's theorem to ideal convergence scenarios and proves its independence from ZFC in these contexts.

Findings

Generalized Egorov's statement is independent of ZFC for various ideal convergence types.

The work broadens understanding of Egorov's theorem beyond classical measure theory.

It establishes foundational results on the limits of ZFC in convergence theorems.

Abstract

We consider the generalized Egorov's statement (Egorov's Theorem without the assumption on measurability of the functions, see \cite{tw:nget}) in the case of an ideal convergence and a number of different types of ideal convergence notion. We prove that in those cases the generalized Egorov's statement is independent from ZFC.